1. Prepare the Crust:

1. Make the pasta dough: On a clean surface, mound the flour and make a well in the center. Crack the eggs into the well, add olive oil and a pinch of salt. Gradually incorporate the flour into the eggs until a dough forms. Knead for about 8-10 minutes until smooth. Wrap in plastic and rest for 30 minutes.
2. Prepare the filling: In a bowl, mix ricotta, Parmesan, lemon zest, lemon juice, salt, and pepper until combined.
3. Roll out the pasta: Divide the dough into 4 pieces. Using a pasta machine, roll each piece through progressively thinner settings until about 1/16-inch thick. Lay sheets on a floured surface.
4. Assemble the ravioli: Place teaspoon-sized dollops of filling about 2 inches apart on one pasta sheet. Brush edges with water, place a second sheet on top, and press around each mound to seal. Cut into squares with a ravioli cutter or knife.
5. Cook the ravioli: Bring a large pot of salted water to a boil. Add ravioli and cook for 3-4 minutes until they float. Drain gently.
6. Make the burst tomatoes: While ravioli cook, heat 2 tablespoons olive oil in a skillet over medium-high heat. Add cherry tomatoes and garlic, cook until tomatoes burst and soften, about 5 minutes.
7. Assemble the dish: Place cooked ravioli on plates. Top with burst tomatoes and garlic. Tear burrata over each portion and garnish with fresh basil.