Make the filling: Pulse peas, parmesan, ricotta, zest, mint, garlic, salt, and pepper in a food processor; with the motor running, slowly drizzle in olive oil until smooth. Refrigerate filling until ready to use.
On a lightly floured surface, divide Pasta Dough into 4 balls. On a lightly floured surface and working with 1 disk of dough at a time, roll dough into an 8"-long oval; dust on both sides with flour. Using a pasta machine, pass dough through machine twice, using the widest setting. Using the next narrower setting, pass dough through machine twice more. Continue to roll dough, setting the rollers to the next narrower setting, until dough is 1⁄16" thick. With a long side facing you, place 2 tsp. mounds of filling along middle of dough, spacing the mounds about 1" apart. Brush dough with water. Take another sheet of pasta and lay it over the other sheet of pasta and mounds of filling; press dough to seal, squeezing out air pockets around filling. Using a pastry cutter or knife, cut out ravioli; transfer to a parchment paper-lined baking sheet. Repeat with remaining dough and filling. Leave ravioli at room temperature for 1 hour to dry.
Bring a large pot of salted water to a boil. Cook ravioli until al dente, 4-5 minutes. Meanwhile, melt butter in a 12" skillet over medium-high. Add prosciutto and cook until crisp, 3 minutes. Add peas and pea shoots 1-2 minutes more. Using a slotted spoon, transfer ravioli to skillet, along with 1⁄2 cup cooking water, zest, juice, salt, and pepper; toss to combine. Transfer ravioli to a serving platter; garnish with mint and parmesan.