Preheat the oven to 450 degrees F. Bring a large pot of salted water to a boil. Put 2 pieces of foil side by side on a baking sheet. Put the almonds on one piece of foil and the broccoli on the other. Transfer to the oven; roast until the almonds are lightly toasted, about 7 minutes. Remove the foil with the almonds. Continue roasting the broccoli until tender, about 7 more minutes. Season the broccoli with salt and pepper and transfer to a large bowl.
Add the pasta to the boiling water and cook as the label directs. Meanwhile, pulse the almonds in a food processor until finely chopped; with the motor running, add the garlic and process until finely chopped. Drizzle in the olive oil and process until blended. Add the basil and pulse until smooth; transfer to the bowl with the broccoli.
Put the tomatoes and half of their juice (about 1 cup) in the food processor and pulse until pureed. Add to the bowl with the broccoli mixture and stir to combine. Add 1 teaspoon salt and 1/2 teaspoon pepper. Drain the pasta and toss with the sauce.