Preheat the oven to 425 degrees F (220 degrees C).

Drizzle olive oil over the bottom of a 9x13-inch casserole dish. Pour tomatoes and their juices into the dish; cut each tomato into 3 pieces. Sprinkle in onion, garlic, red pepper flakes, and 2 teaspoons oregano; stir to combine.

Roast in the preheated oven for 1 hour. Remove dish from oven, stir briefly, return to oven and roast for an additional 15 minutes.

Transfer roasted tomato mixture to a saucepan; pour in water. Process mixture with an immersion blender or potato masher until desired sauce consistency is reached. Stir in 1 teaspoon oregano. Season with salt and black pepper to taste. Set aside.

Fill a large pot with lightly salted water and bring to a rolling boil over high heat. Once water is boiling, stir in ditalini and return to a boil. Cook pasta uncovered, occasionally stirring, until pasta has cooked through but is still firm to the bite, 8 to 10 minutes. Drain well and return to pot.

Pour tomato sauce over ditalini; stir to combine. Stir in goat cheese.