Heat ghee in a stainless steel skillet over medium-high. Sear thighs until well browned on both sides, then remove — chicken will finish cooking in the sauce.
Add mushrooms, onion, and a pinch of salt. Cook over medium-high until liquid evaporates and the fond is deglazed.
Reduce heat to medium-low, add shallots, and sweat a few minutes.
Add garlic and sweat briefly, then pour in cream. Bring to a simmer. Meanwhile, start pasta water.
Dice reserved chicken and add to the simmering cream. Cook until sauce thickens.
Thaw spinach by covering with boiling water; drain in a sieve and chop if whole-leaf. Add to sauce.
Cook pasta until al dente, reserving some pasta water. Add pasta to sauce with splashes of pasta water to bring it together.