Heat the olive oil in a large heavy sauce pan over medium heat. Add the onions and cook, stirring often, until they begin to soften. Add the carrots and celery and cook for 2 mintues. Add the garlic and cook until fragrant; take care not to burn. Add the meat and cook, chopping into fine pieces, until meat is no longer pink and is beginning to brown. Add the Italian seasoning mix and stir in the black and green olives; add the cherry tomatoes.

Measure out 1/2 cup chicken broth and mix well with the tomato paste. Add this mixture to the saucepan, bring to a simmer, lower the heat, and cook until the tomates just begin to break down, adding up to 1/2 cup chicken broth if the sauce is too thick. Stir in the artichoke hearts.

Season to taste with salt and pepper.

Meanwhile, cook penne pasta according to package directions. When the water returns to the boil after the pasta is added, stir in the broccoli florets and cook to desired degree of doneness. Using a slotted spoon or strainer, remove broccoli to a bowl of cold water to stop the cooking process; strain.

When the pasta is just al dente, pour it into a large collander and shake to remove as much water as possible. Add the pasta to the sauce pan and stir to incorporate; the pasta will absorb some of the sauce, which will prevent it from clumping later. Stir in the broccoli and torn basil. Serve at once, passing the parmesan cheese and crushed pepper flakes at the table.