Bring a large pot of salted water to a boil.
Meanwhile heat a large, nonstick or cast iron skillet over medium-high heat, and brown the sausage, breaking it up as you go. (I like to cook long enough to see some crusty edges.) Remove pan from the heat.
When the water boils, add the pasta and bring the water back to a boil. When the water is boiling again, add the broccoli florets, return to a boil once more, and cook according to the pasta instructions for al dente, stirring occasionally. (Note: this will likely cook the broccoli far longer than you usually cook it. This is good. In order to create the “pesto” it needs to be very soft.)
When pasta is almost done cooking, reserve 1 cup of the pasta water and set aside. Drain the pasta and broccoli in a colander, and let it sit for the time being.
Return the empty pasta pot to the stove, add the olive oil, and heat it over medium heat. Add the garlic and optional red pepper flakes. Cook until the garlic is aromatic but not browned, about 30-60 seconds. Reduce the heat to low, and add the pasta and broccoli back to the pot along with the cooked sausage.
Toss to combine, sprinkle the grated cheese and salt and pepper to taste over top (I use a slightly rounded 1/4 teaspoon each of salt and pepper). Mix well and gently mash any large pieces of broccoli. Add 1/2 cup of the reserved pasta water and mix again, adding more cooking water if needed.
Serve in pasta bowls, sprinkle with optional tomatoes, and pass additional grated cheese at the table, if desired.