Handmade Orecchiette With Mortadella and Pea Sauce

Mound 1 2/3 cups flour into a 7"-wide circle on a clean work surface. Form a 3" well in the center. Add eggs, oil, and salt to the well. Using a fork, slowly incorporate flour closest to well to make a paste, gradually pulling in as much flour as you can with the fork. Using a bench scraper or your hands, incorporate remaining flour, then knead with your hands, adding 1 tsp. water at a time if necessary, until a smooth, pliable dough forms.
Fold top of dough toward you, then press down with the heel of your hands. Rotate dough 90 degrees. Continue kneading with this motion until dough is very smooth and elastic, about 10 minutes. Form dough into a ball, cover with plastic wrap, and let sit at room temperature at least 30 minutes and up to 4 hours.
Using bench scraper or knife, cut ball into 3 equal-sized pieces. Pinch off a walnut-sized piece from 1 piece to work with, then wrap all remaining dough tightly in plastic wrap. Starting from the center outward, roll walnut-sized piece into a long, thin rope about 1/3" wide, preferably on a wooden surface to make rolling easier. Using the tip of a sharp knife, cut rope into 1/3" pieces, then position them cut sides up. Using 2 fingers, press down to form 2 little indentations in a thin, flattened oval disc about 1/8" thick. Repeat with remaining dough, covering dough and formed orecchiette with plastic as you go. Lightly toss orecchiette with flour, then cover with plastic and let sit at room temperature up to 4 hours.
Heat oil over medium-low in a large skillet. Cook garlic, stirring, until fragrant, about 2 minutes. Add stock and bring to a boil, then reduce heat to medium and whisk in butter, 1 piece at a time. Cook until sauce is thickened and creamy, 8-10 minutes. Immediately stir in mortadella and lemon zest; season with salt and pepper. Keep warm over very low heat.
Cook orecchiette in a large pot of generously salted boiling water just until pasta floats and is cooked through, 2–3 minutes. Using a slotted spoon, transfer pasta to skillet with sauce. Increase heat to medium, then add peas, half of the mint, and 4 Tbsp. cheese. Toss gently to coat; season with salt and pepper. Divide pasta among bowls and top with remaining mint and 2 Tbsp. cheese.