Preheat oven to 425°. Place the prepared broccoli and garlic slices on a baking pan. Drizzle 3 tablespoons of olive oil over the broccoli. Toss the broccoli and garlic to coat evenly with the olive oil.
Spread the broccoli into an even layer over the baking pan. Season with 1/2 teaspoon salt and black pepper to taste. Toss the broccoli again then spread back into an even layer.
Roast for 10 minutes, turn the broccoli and garlic, then continue roasting for 5 more minutes, or until tender and the edges are crisped.
While the broccoli roasts, place the cherry tomatoes on another baking pan. Toss with 1 tablespoon of olive oil, dried basil, 1/4 teaspoon salt, and black pepper to taste.
Roast tomatoes for 10 minutes, turning once halfway through roasting.
Gently toss together the roasted broccoli and tomatoes, season with additional salt and pepper if desired, then serve.