Preheat oven to 400°F.
Heat EVOO over medium heat in a sauté pan and add butter. When it foams, add garlic, thyme, parsley and black pepper; swirl for a minute or 2.
Place bread cubes in a large bowl, toss with butter sauce and half the cheese. Arrange on a baking sheet and bake until deeply golden and crispy, 20 minutes. (Croutons can be stored in foil at room temp or in an airtight container for several days.)
Bring a couple of inches of water to a boil in a deep skillet. Salt water and add broccoli; cook to tender-crisp, 5 minutes, and drain. (Broccoli can be stored in a plastic bag for several days.)