1 pint grape or cherry tomatoes, halved
1 head broccoli florets or 2 bunches broccolini, trimmed and cut into 1-inch pieces (about 4 cups)
1/2 pound cremini mushrooms, trimmed and sliced (about 3 cups)
1/4 cup olive oil, plus more as needed
1 1/2 teaspoons dried oregano
1 teaspoon red-pepper flakes
3/4 pound bulk spicy or sweet Italian sausage (or fresh sausages removed from casing)
1/4 cup plus 2 tablespoons grated Parmesan, plus more for serving
1 loaf soft Italian bread, split lengthwise
3 to 5 small garlic cloves, grated or minced
Heat the oven to 400 degrees with one rack in the lower third and one in the upper. On one sheet pan, combine the tomatoes, broccoli and mushrooms with 1/4 cup oil. Season with 1 teaspoon oregano, 1/2 teaspoon red-pepper flakes and salt to taste. Toss to combine, then arrange the tomatoes so they are cut-side up. Roll the sausage into 1-inch balls. (There should be about 30.) Distribute them around the vegetables. Sprinkle the entire sheet pan with 2 tablespoons Parmesan. Roast for 15 minutes.
Meanwhile, brush the cut sides of the bread with about 2 to 3 tablespoons of oil. Spread the grated garlic on the bread, then sprinkle with the remaining 1/2 teaspoon red-pepper flakes, 1/2 teaspoon oregano and salt to taste. Cut into 3- to 4-inch pieces. Grease another sheet pan with olive oil, then place the bread on the pan, cut-side up.
After 15 minutes, gently shake the pan to flip the meatballs. Sprinkle the entire pan with the remaining 1/4 cup Parmesan, concentrating your efforts on the tomatoes and the empty pan edges so that some Parmesan has room to crisp. Return the meatball sheet pan to the lowest rack and place the bread sheet pan on the higher rack. Roast until the bread is golden at the edges, the broccoli tips are crispy and the meatballs are cooked through, 7 to 10 minutes. (If the broccoli and meatballs need a little more time, remove the bread from the oven, cover loosely with foil and continue to roast the other sheet pan for 5 more minutes.)
Use a wooden spoon or spatula to scrape up any cheese that has stuck to the bottom of the pan. Serve everything with the garlic bread and more grated cheese.