Pasta Bolognese

I made this based on a few recipes I saw. I modified the ingredients from what I actually used given my view of the results, which were great (but a few small mods can't hurt, right?). I want to try this with some stew beef and shred it, which sounds like a very good idea (I'll post that when I do it!).

Ingredients:
4 medium carrots, quartered and chopped
3 stalks celery, sliced in half lengthwise and chopped
1 medium onion, chopped
2 hot cherry peppers (or equivalent) chopped
1 pound of chopped beef (or veal, lamb, pork or a combination)
10 sprigs fresh thyme, tied together
1 sprigs fresh rosemary, tied together (with thyme is OK)
1 teaspoon hot pepper flakes
1 28-oz can San Marzano (or plum) tomatoes, crushed with juice
Olive oil
Salt and pepper
1/2 cup red wine

Directions:
Heat large pan over medium-high heat and sautee carrots, celery, onion and hot peppers in olive oil with some salt and pepper for 3-4 minutes to soften. Move veggies to the edges of the pan and add meat into the middle and break into big chunks. Let sit for a few minutes to brown the meat, then stir the meat to brown other parts in a similar manner. When it is fully browned, break into smaller chunks and mix with vegetables. Add wine and reduce 1-2 minutes then add tomatoes, rosemary, thyme and red pepper flakes. Bring to a boil, stir well, cover and cook for 40 minutes, stirring occasionally.

Cook your favorite pasta (spaghetti is a classic, though I like the wider pasta such as fettucini or pappardelle) 2-3 minutes less than package instructions for al dente. Just before taking the pasta out, remove 1 cup of the pasta water and add it to the sauce. Transfer pasta to the dish with the sauce and combine, cooking an additional 2-3 minutes.

Serve with grated cheese.