To Make the Cavatelli Dough
In the bowl of a stand mixer fitted with a dough hook, combine the all-purpose flour, semolina flour, and salt.
Add the beaten egg and ricotta cheese.
Knead on medium speed for 5-7 minutes, until the dough is smooth and forms a ball. If the dough is too sticky, add a tablespoon of flour at a time.
Remove the dough from the bowl, wrap it tightly in plastic wrap, and let it rest in the refrigerator for at least 30 minutes.
Once rested, form the cavatelli using a cavatelli machine according to the manufacturer’s directions. Alternatively, roll the dough into thin ropes, cut into ½-inch pieces, and press each piece with your thumb against a gnocchi board or the tines of a fork to create a curl.
To Make the Sauce & Assemble
Bring a large pot of generously salted water to a boil.
While the water heats, place a large sauté pan over medium heat.
Add the olive oil and the diced onion.
Sauté for 2-3 minutes until the onion is translucent.
Add the sliced garlic and smoked paprika (if using) and cook for another minute until fragrant, being careful not to burn the garlic.
Add the halved tomatoes to the pan.
Season with salt and pepper and toss gently.
Cook for 5-7 minutes, until the tomatoes begin to wilt and release their juices, creating a light sauce.
Stir in the peas and toss to combine.
Remove the pan from the heat and set aside.
Add the fresh cavatelli to the boiling water.
Cook for about 3-4 minutes, or until they float to the top. If using dried pasta, cook according to package directions.
Before draining the pasta, reserve ½ cup of the starchy pasta water.
Drain the pasta well.
In a large bowl, toss the hot, drained pasta with the room temperature butter until it melts and coats the cavatelli.
Season with a little more salt and pepper.
Pour the tomato and pea mixture over the pasta.
Add a splash of the reserved pasta water to help the sauce come together and toss everything well to combine.
Add more pasta water as needed to reach your desired consistency.
Taste and adjust seasoning, adding the red pepper flakes if you like a bit of heat.
Divide the pasta among warm bowls.
Top each serving with a generous dollop of ricotta, a sprinkle of fresh mint, and a grating of Parmigiano-Reggiano, if desired.
Serve immediately.