In a large skillet, heat the oil over medium high heat. Sprinkle the chicken with pepper and 2 teaspoons of the salt. Cover the chicken in flour and shake off any extra.
Work in batches and place chicken in skillet to cook. Turn once until golden brown and a thermometer inserted reaches 165 degrees. Transfer to a plate to cool and set aside.
Reduce heat to medium and melt the butter in the skillet. Add shallots and garlic and sauté. Stir often until everything is softened. Add wine and scrape up any bits from the bottom of the skillet. Simmer until liquid is reduced by about half. Add cream and cook, stirring frequently, until mixture coats the back of a spoon.
Remove the pan from heat, add spinach and remaining salt. Stir until spinach is wilted.
Cut chicken against the grain into diagonal strips about an inch wide and 2-3 inches long. Return to the skillet and sprinkle with parsley and serve with the lemon wedges.