Combine cherry tomatoes, oil, garlic, salt, and black pepper in a saucepan over medium-low heat. Cook and stir until garlic is just toasted, 2 to 3 minutes.
Pour chicken broth into tomato mixture; bring to a simmer and cook until tomatoes start to collapse and burst, about 10 minutes. Stir in oregano and red pepper flakes. Purée tomato mixture with a stick blender until sauce is smooth. Cover to keep warm and set aside.
Bring a large pot of lightly salted water to a boil; add penne and cook, stirring occasionally, until tender yet firm to the bite, about 11 minutes. Drain.
Add penne to tomato sauce in the saucepan; stir until penne is well coated with sauce. Stir in Parmigiano-Reggiano cheese; season with salt and pepper.