1. Melt 3 tablesppons butter in a heavy medium skillet over medium heat. Mix in onion. Cover; cook until softened but not brown, stirring occasionally, about 10 minutes. Add 3/4 cup broth; simmer untill onions are tender, about 6 minutes. Puree in processor until smooth. Paur into small saucepan. Add 1 tablesppon butter. Then with more broth if desired.
*Can be made 1 day ahead. cover; chill.
Mix flour and salt in large bowl; make well in center. Add eggs, yolks, and 1 tablesppon water to well.; stir to blend. Gradually stir flour into egg mixture. Knead dough in bowl until shaggy, sticky dough forms, about 5 minutes. Turn dough onto lightly floured work surface and knead until smooth, about 10 minutes. Gather dough into ball. Cover with plastic and let rest 1 hour at room temperature.
Cook butter in heavy samll saucepan over medium heat until brown, about 3 minutes. Pour into small bowl; cool. Mix in ricotta, blue cheese, parmesan, salt, and egg yolk.
Divide dough into 4 equal pieces. Cover pieces 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 setting after every 2 passes and dusting with flour as needed to keep from sticking, until pasta sheet is 24 inches long (sant 1/16 inch thick). Using 2 1/2 round cutter, cut out 12 to 14 rounds. brush half of each round lightly with egg white.
Drop 1 teaspoon filling into center of each round; lift sides of round up over filling to meet at center; pinch to seal along seam, forming dumpling. Repeat with remaining rounds. Place in single layer on lightly floured parchment-lined baking sheets. Repeat with ramining dough.
*Can be made 6 hours ahead; chill.
Working in 2 batched, cook pasta in large deep skille of boiling salted water until just tender, about 5 minutes. Using slotted spoon, transfer to large bowl. Drizzle with 1 tablespoon olive oil; toss gentle. Rewarm sauce; drizzle onto each plate. Top with ravioli and garnish.