Heat three to four cups water in a small saucepan.
Heat a tablespoon olive oil in a large skillet over medium heat. Add two teaspoons garlic and the red pepper flakes. Cook for a minute or two until aromatic.
Add one cup of the hot water and stir in the cauliflower and a large pinch of kosher salt. Cook, stirring for three minutes.
Add the rigatoni, a pinch of salt and continue to stir in ½ cup portions of the hot water, stirring regularly. Add additional water each time the water is mostly absorbed.
Prepare the breadcrumbs: Heat a tablespoon olive oil in a small skillet over medium heat. Add the last teaspoon of garlic and cook until aromatic. Add breadcrumbs and stir until browned. Remove from the heat and stir until no longer browning. Add half of the Parmigiano Reggiano. Add salt and black pepper to taste along with a tablespoon of parsley. Hold aside.
Check the pasta’s doneness after fifteen to twenty minutes of adding water and stirring. It should be just al dente. Taste for seasoning. Drizzle in a tablespoon of olive oil. Add the olives, stir and remove from the heat. Stir in the remaining cheese, parsley and chives.
Serve in individual bowls topped with the breadcrumb mixture.