Prepare the Dough: In a bowl, mix gluten-free flour and salt. Create a well in the center, add eggs and olive oil, then mix until a dough forms. Knead for 5 minutes, wrap in plastic, and let it rest for 30 minutes.
Make the Filling: In a bowl, combine ricotta, Parmesan, salt, black pepper, garlic powder, and oregano. Mix well and set aside.
Roll the Dough: Roll the dough into a thin sheet (about 2mm thick). Use a round cutter to cut circles.
Fill the Tortellini: Place 1/2 teaspoon of filling in the center of each dough circle. Fold in half to form a half-moon, press edges to seal, then wrap around your finger and pinch ends together.
Cook the Tortellini: Bring a pot of salted water to a boil. Drop in tortellini and cook for about 3-5 minutes, or until they float.
Serve: Drain and serve with your favorite sauce, such as marinara or browned butter with sage.