On a clean surface, mound the flour and create a well in the center. Crack the eggs into the well, add olive oil and a pinch of salt. Using a fork, gradually incorporate flour into the eggs until a shaggy dough forms.

Knead the dough for about 8–10 minutes until smooth and elastic. Wrap in plastic wrap and let rest at room temperature for 30 minutes.

In a bowl, mix ricotta, mozzarella, provolone, Parmesan, salt and pepper until creamy.

Divide dough into two portions. Roll each piece into a thin sheet (about 1/16 inch thick), dusting with flour as needed.

Place teaspoon-sized mounds of filling 1 inch apart on one sheet. Brush around each mound with water, then lay the second sheet on top. Press firmly around filling to seal and cut into individual ravioli.

Bring a large pot of salted water to a gentle boil. Cook ravioli in batches for 3–4 minutes, or until they float to the surface. Remove with a slotted spoon.

In a small saucepan, combine pesto and heavy cream over medium heat. Stir until warm and slightly thickened, about 2–3 minutes.

Plate the ravioli, spoon over the pesto cream sauce, and garnish with fresh basil.