Carrots are one vegetable that I seem to have trouble cooking just right for Lyra...even when I think I have boiled or roasted them to death the centre still seems too hard for her 4 little teeth to bite. Recently, though, I have noticed that when they are in a stew, slow cooked for hours and super duper soft she will gobble them up like it is no body's business (in fact last night they were the first thing she ate on her plate!). It is the same with other hard root veg like parsnips (although she likes those roasted) and turnips. I don't blame her sometimes I can't stomach those either unless they are super soft and drenched in butter, but in a stew they are just...well...different.
My go-to stew uses this recipe from Jamie Oliver's Ministry of Food. It is so simple, just chop and dump the veg, sautee a bit until the onions are soft, chuck in the stewing beef and some flour, mix that all up and then in with a carton of chopped tomatoes and (this is where it is different from Jamie's recipe) 400ml of chicken stock. Into the oven for about 3 hours and voila!
I like to mix up the veg and use parsnips, turnips, potatoes, carrots and celery (about 3 cups total chopped) and then 1 onion chopped. Sometimes I scoop out the veg and meat and divide it up on a plate for Lyra and sometimes I just scoop it all into a bowl the way the adults have it. Either way she usually gobbles it all up and asks for MORE.