Orecchiette With Peas And Shrimp Or Chicken

I like to make this using leftover chicken or turkey!

12 ounces orecchiette or medium shell pasta
8 ounces cooked baby shrimp, partially thawed if frozen OR cooked chicken
1 cup tiny green peas, partially thawed if frozen
4 large eggs
1/2 teaspoon kosher salt
Freshly ground black pepper
2 tablespoons unsalted butter
1/2 to 1 cup heavy cream (to taste)
1/4 cup freshly grated Parmigiano-Reggiano cheese
2 tablespoons minced fresh chives

Cook pasta in a large pot of boiling salted water until almost al dente, 10 to 15 minutes, depending on pasta shape. Stir in shrimp and peas and cook for 1 minute more; drain.

Whisk together eggs, salt and a grinding of pepper in a medium bowl. In a large skillet, melt butter over low heat. When foam subsides, add eggs and cook, stirring until creamy but not quite cooked, about 3 minutes. Add pasta mixture, cream, salt and pepper, cheese and chives. Heat, stirring until pasta absorbs some of the cream. Spoon into a bowl and serve at once.