If available, cook this in an oven safe Dutch oven with a cover so that the cheese can go under the broiler. If that’s not available, any large brazier or saute pan with a cover will do.
Over medium-high heat, add the olive oil to the pan. Once hot, add green peppers and onion. Saute for 5-10 minutes, until just softening. Then add the Italian sausage and minced garlic, cooking until the sausage is browned. From here, drain if necessary.
Add diced tomatoes, tomato sauce, chicken stock, and salt and pepper (including the pepper flakes). Bring to a boil. Add the rice, stirring to combine. Return to a boil, then reduce to a simmer and cover. Allow your wonderful meal to cook for 40 minutes, covered. After 40 minutes, check the texture of the rice, cooking for an additional 5-10 minutes if necessary.
Once the rice is fully cooked, top with shredded cheese. If you are able to put your pan in the oven, cook under the broiler at 475 for 3-5 minutes, until the cheese is perfect and bubbly.
If you are not able to put your pan in the oven, add the cheese and immediately put the cover back on. Allow to sit for 5-10 minutes (and up to 20 minutes, if you are busy), to let the cheese melt.