In a medium bowl, combine ¼ cup of the basil, the ricotta, Parmesan cheese, and 1/3 cup frozen peas. Season with salt and pepper to taste.
Scatter some of the flour over a parchment-lined baking sheet. Lay a sheet of pasta out onto a lightly floured surface. Keep extra pasta sheets covered with damp paper towels to keep from drying out. Use a very sharp knife to trim the sheets into 2 long strips, each about 3-4 inches wide. Cut long sheets into shorter segments to make them easier to work with.
Scoop a scant tablespoon of the ricotta mixture onto 1 strip of pasta, leaving about 1 ½-2 inches of space in between each mound of filling. Fill a small bowl with cold water and use your fingers to spread the water along the edges of the pasta sheets and in between each mound of filling. This will help seal the pasta sheets together.
Gently lay the other pasta strip over the first pasta strip with the filling. Gently press your fingertips around the mounds of filling. Once the strips are sealed together without any air bubbles, use a sharp knife, or a ravioli cutter, to separate the raviolis. Cut in between each mound. Set the raviolis on the prepared baking sheet.
Repeat with the remaining pasta sheets and ricotta mixture until you have 5 raviolis per serving.
Fill a large pot 2/3 high with cold water and bring to a boil.
While you wait for the water to boil, heat the olive oil to medium-high in a medium-sized sauté pan. When warm, add the garlic and dried oregano. Crush the oregano between your fingertips as you add it to the pan. Cook for about 30 seconds, stirring continuously, then add the tomato paste. Toast the paste for another minute or so, continuing to stir. Once the tomato paste is fragrant, stir in the canned tomatoes. Stir until well combined, then bring to a boil. Stir in ¼ cup of the basil, 1/3 cup frozen peas, and heavy cream, then season with salt and pepper to taste. Reduce the heat and let the sauce simmer gently as you finish cooking. If the sauce is too thick, spoon some of the pasta cooking water into the tomato sauce.
Once water is boiling, add 1 tablespoon of salt and gently lower the raviolis into the water. Cook until the raviolis float to the surface and corners are very pliable, about 2-3 minutes. Use a slotted spoon to lift the raviolis out of the water, then transfer them directly to the sauté pan of creamy tomato sauce.
After all of the raviolis have been added to the creamy tomato sauce, remove the pot of water from the heat. Gently stir the raviolis to coat them with sauce, then transfer 5 raviolis to each dinner plate. Scoop some extra sauce over the top, then serve warm with extra Parmesan cheese on the side.