Scallops with stock

1 lb scallops , washed, cut in half if large 3 tablespoons flour , for dredging 1 cup milk 1/2 teaspoon kosher salt (to taste) 1/2 teaspoon pepper (to taste)[...]

5 tablespoons extra virgin olive oil , divided 1 large shallot , finely chopped 12 button mushrooms , thinly sliced 8 tablespoons butter , divided 1[...]