Heat oil in a large skillet over medium high heat. Add garlic, beef and pork; sauté until brown, about 3 minutes. Add spinach and sauté until wilted and liquid has evaporated, about 3 minutes. Cool.
Add the spinach-meat mixture to a food processor, and chop finely. Transfer to a medium bowl. Mix in cheese. Season to taste with salt and pepper. Mix in egg.
Lightly flour a baking sheet. Arrange 12 wonton wrappers on work surface. Spoon 1 teaspoon filling in center of each. Brush edges with water. Fold each wrapper in half, forming a triangle. Press edges together. Using a 2” diameter ruffled cookie cutter, cut edges to form a half moon shape. Transfer to baking sheet. Repeat with remaining wrappers and filling.
Set a large pot of salted water on the high heat to boil. Working in batches, cook agnolotti until just tender but still firm to bite, about 3 minutes. Using a slotted spoon, transfer to a shallow bowl. Spoon parsley butter over all.
Melt butter in a medium saucepan over low meat. Add parsley; keep warm.