Mmm... most ingredients are added to a risotto at the beginning, with onion, or towards the end if they need to be cooked separately, or don't really need any cooking. With carrots, I'd grate them into the risotto at the beginning, with the onion. That should give them enough time to soften, especially if they're grated quite finely. I'd add something else, to complement the carrot; maybe a pinch of saffron, if you're feeling flush (lucky toddlers!), or something green - parsley is a classic. Let us know how it goes down with the critics...
When I've made risotto with carrots, I actually simmer them first and puree them while the rice is cooking, adding the puree near the end of cooking the risotto. It's actually a bit easier than grating, since you just need to cut the carrots into big chunks and toss them into a pot. I add a bit of cider or citrus to the cooking water to brighten up the flavor. (Roasting them might be another way to go to get the sugars to concentrate more, but I've never tried it this way)
You might look for squash or pumpkin risotto recipes for suggestions of flavor combinations that go well with root vegetables. They can go from sweet (cinnamon, citrus and even a little bit of honey) to savory (sage, parmesan, etc.), and all sorts of combinations in between!
Paraphrased from Italian Vegetarian, Jack Bishop
Golden Risotto with Carrots and Peas
3 c. carrot juice and 3 c. water warmed
3 T evoo
1 onion, chopped
2 garlic cloves, minced
2 c. rice (he calls for Arborio, but whatever you usually use for your risotto)
1/2 c. white wine
4 med carrots, peeled, chopped
2 c fresh or frozen peas (thawed if frozen)
Parsley, butter, parmigiano-reggiano cheese to finish
Saute onions over medium heat until translucent. Stir in garlic and cook for an additional minute. Stir in rice and cook for 1 minute. Add wine and simmer, stirring constantly, 1 to 2 minutes (until wine aroma is gone).
Add carrots and 1/2 c. carrot/water mix. Continue the typical risotto process of 1/2 c liquid at a time until rice is almost al dente.
Stir in peas and parsley, add more liquid as necessary until rice is soft but still a bit al dente.
Remove from heat. Stir in cheese and butter. S/P to taste.
if it is solely to get your kids to eat carrots - risotto is a a bit of an effort - do you have a rice cooker? what i do for my kids is: in a rice cooker with japanese rice i add grated carrot and zucchini - very little prep - turn it on and in 30 minutes later it is done. you can freeze packets and microwave them on demand. they can eat it out of a bowl or you can form small rice balls - they like to pick up the balls themselves - the japanese rice is a bit sticky so it forms balls nicely.
Thanks for the tips... I'm always looking for new somewhat-healthy side dishes for my little guys. We do a carrot orzo they like (similar to howchow's idea above but with orzo rather than the sticky rice). Was going to try to make the risotto above (the one with the carrot juice) last night but sadly realized I didn't have the risotto rice at home. Will try soon once I get to the store... Thanks again.