1. Put ham hock in a saucepan, add enough water to cover by an inch, and bring to a boil over high heat. Boil for 2 hours, adding more water if needed to keep hock covered. Drain and set aside until cool enough to handle. Remove meat from bone; discard skin, bone and fat. Roughly chop meat.
2. Meanwhile, heat broiler. If using chiles, broil on a baking sheet, turning occasionally, until charred all over. Remove from broiler and reduce oven temperature to 350 degrees . Transfer chiles to a plastic bag and close bag to steam them for at least 5 minutes. Rub off and discard skins. Slit chiles, discard stems and seeds, and mince.
3. Spread breadcrumbs on a baking sheet and toast at 350 degrees for about 10 minutes, until golden. Season with 1/2 tsp of the salt and 1/4 tsp of the pepper and set aside.
4. Bring a large pot of water to a boil over high heat. Add 1 tbsp kosher salt per quart of water. Add pasta and cook 2 minutes longer than time indicated on box. (This is grown-up kid food, not an al dente dish.) Drain pasta; set aside.
5. Put carrots in a saucepan, cover with water and boil until tender, 5 to 6 minutes. Reserve 1/4 cup of the liquid and drain carrots. Allow carrots to cool slightly, then transfer to a blender. Add 1 tbsp of the reserved liquid. Puree until smooth, adding remaining liquid gradually as you puree. Season with remaining 1/2 tsp salt and 1/4 tsp pepper.
6. In a large saucepan, bring milk to a simmer over medium-high heat. Reduce heat and let simmer until you're ready to use it.
7. Make a light roux: In a medium skillet, melt butter over medium heat. Add flour and cook 3 to 4 minutes, stirring constantly, until it turns a light nutty color. Scrape roux into simmering milk, whisking constantly until no lumps remain and sauce begins to thicken. Stir in carrot puree. Slowly add cheddar, whisking all the while. Add chopped hock meat, chiles (if using) and pasta and stir to combine. Transfer mac and cheese to a large baking dish or cast-iron skillet. You can prepare dish to this point several hours in advance; cover with foil and keep at room temperature until you are ready to bake it.
8. If you've just made the mac and cheese and it's still warm, sprinkle breadcrumbs on top and bake at 350 degrees for 15 to 20 minutes, until top is golden brown and crunchy. If you made the mac and cheese in advance, heat it in a 350 degrees oven for 40 minutes. Sprinkle breadcrumbs over top and bake an additional 15 minutes, until top is golden and crunchy.