In a small saucepan set over low heat, cook the shallots in butter until translucent.
Transfer to a medium bowl and combine with the remaining filling ingredients.
Make the pasta:
Make a well with the flour and salt.
Beat the eggs and olive oil in the well with a fork and begin slowly incorporating the flour with a swirling motion, eventually switching to a bench scraper (one of my favorite all-purpose kitchen tools). You probably won't need all of the flour (save it). Start forming a ball with your hand and squeeze the dough together with your fingers. You want the dough to be a bit "tacky," as they called it in school. Not quite sticky, but you want resistance. You don't want it too dry.
Once the dough is formed, wrap it in plastic and allow it to rest in the refrigerator for at least 30 minutes.
If you don't have a pasta machine, you can use a rolling pin, but a machine will make the job easier. I have an Imperia. Either by hand or machine, roll out thin strips of pasta, incorporating the reserved flour as needed. Thinner pasta dough makes better ravioli. If using a machine roll to the thinnest setting.
Sprinkle some semolina flour onto a cutting board to prevent the pasta from sticking while assembling the ravioli.
Assemble the ravioli:
To assemble the ravioli you need egg wash, more semolina and a round cookie cutter. Egg wash one sheet of pasta and use the large cutter to gently map out a row of ravioli without actually cutting them. Drop about a teaspoon of filling in the center of each ravioli.
Bring a second sheet of pasta over the first, slowly pressing the dough around the filling and removing the air.
Use the large cookie cutter to cut each ravioli. Hand press the edges, sprinkle both sides with semolina flour and allow to dry for a bit before cooking. This ravioli will cook much faster than the store-bought variety, only a few minutes.
Make the sauce:
Melt the butter in a saucepan over medium-low heat. As the butter begins to simmer, begin whisking constantly until the milk solids begin to brown. This will take about 5 minutes.
Once the milk solids begin to brown, add the chicken stock and reduce the heat, allowing the sauce to simmer and thicken a bit. Season with salt and pepper to taste.
Serve the warm brown butter sauce drizzled over the cooked ravioli.