Make a well with your hands in the center of the flour.
Add the whole eggs, egg yolks, and olive oil to the well.
Slowly incorporate flour from around the edges.
Using a fork or a wooden spoon, mix the raw ingredients into a dough.
Knead the dough until it is soft and pliable.
Wrap the dough ball in plastic wrap and let it sit in the refrigerator for an hour or until you’ve prepared the other components.
Create the filling
Add milk to a saucepan and place it over low heat until it gets warmed up.
Add diced cheese and continue stirring until the cheese melts.
Take the saucepan off the heat and let the cheese mixture cool down.
Add the egg yolk and butter and mix well.
Place the saucepan back on low heat whisking constantly to let the filling thicken.
Once it thickens to your liking, take it off the heat and let it cool.
Assemble the pasta
Once the dough has rested, take it out of the plastic and roll it using a pasta machine.
Place it on a floured surface and trim the edges to form a rectangle.
Using a teaspoon, scoop the cheese mixture and place it on the edge of the pasta sheet. Make sure you have at least a 2-inch gap between each dollop of filling.
Brush the sides of the pasta sheet with egg wash or water.
Fold the sheet over the filling and using your fingers, make dents to form small pockets.
Using a pasta cutter, cut the agnolotti into equal sizes. Apply some pressure with your fingers so they won't open.
Fill a pot with water and place it over high heat. Add salt and bring the water to a boil.
Once it starts boiling, add the agnolotti and cook for four minutes or until they float to the surface.
Strain the pasta and place them on a serving dish.
Make the brown butter sage sauce
Place a pan over medium heat and add diced unsalted butter.
Once the butter starts to melt, keep an eye on it until it begins to foam.
Once it reaches that point, add fresh sage leaves, spreading them across the pan.
Let them sit for 3 to 5 minutes or until the butter starts to brown.
Either toss the Agnolotti Del Plin in the butter, pour the butter over the dish, or serve it separately.