Bring first 4 ingredients to boil in small saucepan. Cook uncovered until peas are just tender, about 3 minutes. Cool slightly. Transfer mixture to blender; puree until smooth (sauce will be thin). Season with salt and pepper. DO AHEAD Can be prepared 6 hours ahead. Cover and chill. Rewarm before using.
Cut top 3 inches off asparagus; cut into 1/2-inch lengths. Cook in saucepan of boiling salted water until tender, about 3 minutes. Drain; place in bowl of ice water. Drain; pat dry. Mix cheese and mint in medium bowl. Stir in asparagus. Season with salt and pepper; mix in egg.
Place flour in processor. Add eggs. Using on/off turns, blend until clumps of moist dough form (do not process into ball). Turn dough out onto lightly floured work surface; shape into ball. Knead until smooth, sprinkling lightly with flour if sticking, about 3 minutes. Wrap in plastic. Let rest at room temperature at least 20 minutes and up to 2 hours.
Cut dough into 8 equal pieces. Cover with plastic wrap. Set pasta machine to widest setting. Flatten 1 dough piece into rectangle; run through machine. Fold in half crosswise (end to end) and run through again. Continue, adjusting machine to narrower settings after every 2 passes and dusting with flour as needed to keep from sticking, until pasta sheet is 22 inches long (scant 1/16 inch thick). Place sheet on lightly floured work surface; cover with plastic. Repeat with remaining pasta pieces.
Starting 1 inch from 1 short side of 1 pasta sheet, drop ricotta filling by rounded teaspoonfuls down center of sheet, spacing mounds 2 inches apart. Brush pasta edges and between mounds of filling lightly with water. Cover with second pasta sheet, pressing down around filling to eliminate air pockets and to seal. Using fluted pastry wheel, cut pasta between filling, trimming sides to form 2- to 2 1/4-inch ravioli. Repeat with more pasta and remaining filling, making about 36. (Reserve remaining pasta for another use, cutting into shapes and drying on floured work surface.) Place ravioli on floured baking sheet; let dry 30 minutes. DO AHEAD Can be made 6 hours ahead. Cover; chill.
Working in 2 batches, cook ravioli in very large pot of boiling salted water until just tender, stirring gently, about 3 minutes. Drain ravioli. Divide hot pea sauce among 6 plates. Top with ravioli. Drizzle with olive oil and serve.