Heat the oven to 400°F (200°C). In a 9 × 13-inch oven-safe baking dish, toss the cherry tomatoes and roughly chopped garlic with 2 tablespoons olive oil and the black pepper. Tuck the garlic among the tomatoes rather than leaving it exposed on top.

Nestle the drained feta block in the center of the tomatoes and drizzle the remaining 1 tablespoon olive oil over the cheese. Bake on the middle rack for 30–35 minutes, until the tomatoes have split and released juice and the feta is soft when pressed with a spoon. The cheese need not melt into a liquid.

Meanwhile, bring a large pot of unsalted water to a boil. Time the pasta so it finishes near the end of roasting. Cook the penne according to the package directions until al dente. Before draining, scoop out ½ cup pasta water into a heatproof measuring cup. Drain the pasta without rinsing.

Use oven mitts to set the hot baking dish on a heatproof surface. Mash the softened feta and tomatoes with a wooden spoon, keeping clear of hot tomato juices. Stir in 2 tablespoons of the reserved pasta water to start, until the mixture becomes a creamy, slightly textured sauce.

Fold in the hot penne and torn basil. Toss thoroughly, adding more reserved pasta water 1 tablespoon at a time only if needed, until the sauce coats the pasta. Serve immediately in four equal portions.