Make the Dressing:
In a small bowl, mix the chopped garlic with lemon juice and let sit for 5 minutes. On a cutting board, mash the anchovies with 1/8 teaspoon salt into a paste. Add this paste to the garlic-lemon mixture along with mayonnaise, Worcestershire sauce, and black pepper. Whisk well. Taste and adjust with more salt or lemon juice if desired. Cover and refrigerate until needed.

Prepare the Croutons:
Preheat the oven to 400°F. Toss the torn bread pieces with 2 tablespoons of olive oil and 1/8 teaspoon salt in a large bowl. Spread the bread on a baking sheet and bake for 8–10 minutes, until golden and crisp. Let cool.

Cook the Broccoli and Pasta:
Bring a pot of salted water to a boil. Add the broccoli florets and cook for 3–4 minutes, until just tender. Use a sieve to lift out the broccoli and set it aside in a large bowl. In the same water, cook the pasta according to package instructions until al dente. Drain, rinse with cold water, and add to the broccoli. Toss with the remaining 1 tablespoon of olive oil and refrigerate for at least 1 hour.

Assemble the Salad:
Toss the chilled pasta and broccoli with about three-quarters of the dressing. Crush half of the croutons and mix them in along with three-quarters of the Parmesan cheese. Toss until combined.

Serve:
Transfer the salad to a serving bowl. Top with remaining croutons and Parmesan. Serve the remaining dressing on the side.