Another way is to try to understand how flavour affinities work.
Here is an easy way to think about that: Flavours work either in harmony or in opposition, in similarity or in contrast. So you are looking for complementary and contrasting flavours. Remember you are aiming for several layers of flavour, so ideally you'd want a combination of both aspects: a complimentary (similar) flavour will deepen the overall taste, a contrasting flavour will create accents to highlight the taste experience.
Let's take carrots, say.
They are often lurking in the back of the fridge, somehow too common and too boring to be remembered.
Yet carrots have a deep sweetish taste - even when raw and crunchy, more so when cooked, maxxed out when roasted.
This list is not exhaustive, of course, there could be much more, but these are a few that came to my mind straight away, just by thinking in both directions. Also keep in mind that on top of playing with flavours, you can also play with textures (chunky, grated, soft, crunchy) and cooking methods.
Let's get more specific:
1. Grated carrot in salads
Nice in any salad really - adds flavour and colour (and goodness!) Especially good in combination with grated beetroot and/or shredded white cabbage.
Make sure you create contrast with your dressing: lemon juice/zest, ginger, garlic, soy sauce all work really well.
Cabbage & carrot salad is the classic Greek winter salad (when tomato supplies are running low), simply dressed in olive oil and lemon juice.
2. Grated carrot fritters
Be sure to add spices. Use flour, egg and/or ground flaxseed as a binder. Serve with a zesty or spicy dip for contrast.
I don't like the mess of frying so I prefer the non-fry version (this is also low carb and gluten-free as it avoids flour)
3. Carrot soup
Soups are easy and delicious and a great, and carrot soup is no exception. Sweet potato or squash are nice additions to deepen the flavour and the colour. Be bold with the spices to create contrast to the sweetness. Some classic flavour combinations to get you started (but I urge you to make up your own by adding extras):
carrot & coriander
carrot & ginger
carrot & lentil
carrot & sweet potato
4. Roast carrots
Roasting concentrates the flavour, and super easy to do: just throw in a tin with some spices and cooking fat. Also lovely as part of a tray roast.
Honey and thyme and/or cumin is a lovely combination (there we go again with complementing and contrasting).
A bit of butter adds special succulence.
Carrots are a classic 'base layer' ingredient adding depth of flavour to any dish.
Unsurprisingly they are integral to both the French mirepoix and the Italian soffrito - both based on the holy trinity of onion, celery, carrot.
6. Carrot with lentils/chickpeas
A lovely combination whether it's in a soup, a casserole or a stew. The shorter the cooking time the smaller you want to chop them. Don't forget to add some contrast.
7. Carrot hummus
Use cooked carrots (roasted or steamed) in addition or instead of chickpeas to make a dip.
8. Carrot cake
A classic with endless possibilities of flavour combinations.
If you have read that far you'll know why ginger, orange, and raisins/sultanas are such classic flavourings (among many other possibilities - how about cardamom?)
9. Shaved carrot in stir fries
Carrots are not a 'natural' candidate for stir fries as they are dense and don't cook quickly. Unless... you grate or shave them.
They work really well alongside the classic stir-fry flavourings of garlic, ginger and soy sauce, and add a lovely dash of colour.
I use a potato peeler, but if you have a spiraliser in the back of your cupboard, it's a chance to put it to use.
10. Carrot & peas
Forget boiled peas. Gently sauté with onion, diced carrot, garlic and herbs instead.
The French like adding butter and lettuce to this, the Greek prefer olive oil and tomato. Try it!
11. Carrot & kohlrabi
Bonus idea, if you accidentally end up with a weird an wonderful kohlrabi in your veg box: in southern Germany and Austria, kohlrabi with carrots and cream is a classic sauce (Kohlrabi Sahne).
Dice carrots and kohlrabi (I always add an onion), soften in butter or olive oil, flavour with pepper and parsley, add cream at the end to make a sauce.
Works equally well with a piece of meat or fish as it does with plain boiled or baked potatoes, and even pasta.
Btw, if you can find them, carrot tops are edible too! They taste earthy and herby, like a combination of carrots and parsley. That's for another post but here are a couple of quick ideas:
carrot top pesto
use as a green in stir fries and casseroles
use as a herb in soups, salads, and dips/sauces (say in hummus or a green salsa)