Bring 4 quarts water to a boil in a large pot, add pasta and salt, and cook until pasta is al dente, 9 to 10 minutes. Add broccoli and continue to cook until the pasta is tender, 1 minute longer. Drain and set aside.
Meanwhile, whisk oil, vinegar, lemon juice, mustard, honey, and garlic in a large bowl; add 1/2 teaspoon salt and 1/4 teaspoon pepper.
Add drained pasta and broccoli and stir to coat with dressing. Let cool. Mix in tomatoes, olives, basil, parsley, and radicchio; stir to combine. Season with salt to taste.