Ricotta Tortellini

Mash all ingredients in a medium bowl until well blended and smooth. Cover and chill while preparing dough.
Place first 3 ingredients in bowl of a stand mixer with a dough hook. Mix at low speed until dough pulls away from side of bowl, about 4 minutes. Place on work surface; knead until smooth, adding water by teaspoonfuls if dry, 2-3 minutes (dough is fairly stiff). Divide in 4, flatten, wrap in plastic, and chill for 30 minutes.
Working with 1 dough round at a time, run dough through widest setting of a pasta machine. Fold in half; run through machine. Repeat 7 times. Roll through machine without folding, decreasing width setting after each roll, until 1/16" thick. Transfer to a floured surface.
Using a 3" cookie cutter, cut dough into circles. Spoon 1 rounded teaspoonful of filling into center of each dough. Brush edges lightly with egg white; fold over and press to seal, forming a half-moon shape. Fold and press tips together, moistening with egg white to seal. Transfer to a lightly floured rimmed baking sheet. DO AHEAD: Can be made 6 hours ahead. Cover and chill.
Bring a large pot of water to a boil. Season with salt; add tortelloni. Simmer, stirring gently, until cooked through, 2-3 minutes after they begin to float. Using a slotted spoon, divide tortelloni among bowls. Drizzle melted butter over and serve with cheese.