Preheat the oven to 350°F.

Place the chicken breasts between two sheets of plastic wrap and gently pound them to an even thickness of 3/8-inch.

Heat the olive oil in a large pan over medium-high heat. Add the chicken in a single layer (work in batches if necessary) and cook until lightly golden and cooked through, 2-1/2 minutes per side.

Transfer to a buttered baking dish large enough to hold the chicken in a single layer and set aside.

Reduce the heat to medium and add the butter to the pan. Once melted, add the onion and sauté until softened, 3 minutes. Add the garlic and continue cooking 1 minute longer.

Whisk in the flour and cook until well blended and golden in color, 2 to 3 minutes.

Whisk in the sherry until blended, then start whisking in the milk in 1/4 cup increments, blending until smooth after each addition.

Stir in the nutmeg and mustard, then add the spinach.

Continue cooking, stirring often, until the spinach is completely wilted and nicely coated with the sauce, 2 to 3 minutes. Remove from the heat.

Spoon the spinach mixture over the chicken. Top with grated cheese and bake until the cheese has melted, 7 to 8 minutes.