Preheat oven to 375 degrees F (190 degrees C).

Combine tomatoes, olive oil, garlic, salt, and pepper in a bowl until well mixed; spread on a shallow-sided baking sheet.

Bake in the preheated oven until tomatoes are soft and wrinkled, 25 to 30 minutes.

Bring a large pot of lightly salted water to a boil. Cook angel hair pasta in the boiling water, stirring occasionally until tender yet firm to the bite, 4 to 5 minutes. Drain; reserving a small amount of cooking water.

Spoon tomatoes with their juices into a small saucepan; add basil and red pepper flakes. Mix in reserved cooking water to thin tomato mixture to desired consistency. Cook and stir over low heat until warmed, about 5 minutes; stir in pasta. Top with Parmesan cheese before serving.