Cook orecchiette with tablespoon salt to 1 minute short of package time. Reserve 1 cup pasta water; drain.
Meanwhile, season cutlets with 1/4 teaspoon salt and pepper. Heat oil in large skillet; cook 4 to 5 minutes per side to at least 165°F. Rest on board.
Melt butter over medium; cook shallot 2 minutes. Add spinach by handfuls; cook 2 to 3 minutes until wilted and moisture evaporated.
Stir flour into spinach 1 minute; gradually add wine and milk. Gently simmer 3 minutes; add nutmeg and remaining salt.
Slice chicken; return with pasta and 1/4 cup reserved water. Toss over low 1 to 2 minutes. Add Parmesan off heat and more water if needed; serve.