Bring a large pot of salted water to boil. Line a baking sheet with parchment paper and dust with flour.
Beat the eggs with 1 teaspoon salt and several grinds of pepper in a small bowl. Put the ricotta in a large bowl and whisk in the eggs with a fork until smooth. With a wooden spoon, stir in 1/2 cup of the Parmesan. Stir in 3/4 cup of the flour; the dough should be slightly sticky but hold its shape, if not, add flour a tablespoon at a time, but not more than 1 cup in all.
Turn the dough onto a floured countertop and knead just to bring it together. Divide the dough into 4 pieces. Roll one piece into a 1-inch-thick log and cut into 3/4-inch-long nuggets. Press the tops lightly with the tines of a fork. Transfer to the prepared baking sheet. Repeat with the remaining dough.
To finish the gnocchi, melt the butter in a large skillet (use up to 8 tablespoons if you want your pasta saucy).
Add the gnocchi to the boiling water – you may need to do this in batches. Add 1/2 cup of the pasta cooking water to the butter and let simmer while you cook the gnocchi.
Once they float, cook until tender, 2 to 3 minutes. Gently remove with a spider or strainer to the skillet with the sauce. Toss the gnocchi to coat in the sauce. Sprinkle with the parsley and remaining 1/2 cup Parmesan. Remove the skillet from the heat and stir gently to combine.