I've discovered that pretty much any vegetable can be cooked in this manner—lots of olive oil and garlic, and long, slow cooking—and it will turn out well. Great for grown-ups, great for babies, great for all. —Merrill Stubbs
carrots, peeled and sliced into 1/4-inch rounds
fat cloves garlic, peeled and smashed
Combine the olive oil, carrots, garlic, and a couple small pinches of salt in a medium, heavy-bottomed saucepan. Set it over medium heat and bring the oil to a simmer. Give the carrots a good stir, cover the pot, and turn the heat down as low as it will go.
Cook the carrots, stirring gently every once in a while, until the slices are soft enough that they can be smushed easily by gently pinching them between your fingers. (This should take anywhere from 1 to 2 hours.) If at any point you find that the carrots start to stick to the pan and brown, gently lift them from the bottom of the pan, add a few tablespoons of water and re-cover.
When they are very soft, you can serve them as is. Or, if you're feeding a baby (or you just like them this way yourself), you can either mash the carrots gently or push them through a fine-mesh sieve before serving them. Make sure to let them cool before you feed them to a baby!