Mound the 2 cups of flour on a clean work surface and make a deep well in the center.
Crack 3 eggs into the well, add 1/2 tsp salt and 1/2 tsp olive oil, then beat the eggs with a fork while gradually pulling flour into the center until a shaggy dough forms.
Use your hands or a bench scraper to bring the dough together, adding a little more flour if sticky or a splash of water if too dry.
Knead the dough for 8–10 minutes until smooth and elastic, wrap in plastic wrap, and let rest for about 20 minutes.
While the dough rests, make the filling: combine 1 cup ricotta, 1/8 lb finely grated Parmigiano-Reggiano, 1 egg, 2 tbsp chopped basil, and salt and pepper to taste in a bowl; stir until smooth and set aside.
Lightly flour a baking sheet and set aside. Unwrap the dough, cut into four pieces, and keep unused sections wrapped.
On a well-floured surface, roll one section of dough with a floured rolling pin from the center outward, turning frequently, until very thin and long.
Spoon teaspoon-sized mounds of filling about 1½–2 inches apart across the sheet of dough, taking care not to overfill.
Fold the top layer of dough over the filling, press around each mound to remove air, then use a floured ravioli stamp or cutter to seal and cut each ravioli; place on the floured baking sheet.
Gather leftover dough, form into a ball, wrap and rest while you finish the remaining sections.
Optional: freeze trays of ravioli in a single layer for 24 hours, then transfer to freezer bags for storage.
To cook, bring a large pot of salted water to a boil, add ravioli, and stir gently; they are done when they float to the top, then scoop out about 1/2 cup of pasta water and drain the ravioli, returning them to the hot pot (burner off).
In a small saucepan, melt 2 tbsp butter, grate in 1/2 clove garlic, then add 1/4 cup heavy cream, 3/4 cup grated Parmigiano-Reggiano, and salt and pepper to taste; stir 1–2 minutes until the sauce thickens, adding reserved pasta water as needed to reach desired consistency.
Toss the cooked ravioli gently with the sauce and serve immediately, garnished with chiffonade basil if desired.