To make the filling: In a medium skillet heat the oil over high heat and saute the spinach until wilted, about 3 minutes.
Drain the spinach squeeze dry and finely chop. Combine the ricotta, chopped spinach, Asiago, and nutmeg. Season the mixture with salt and pepper.
To make the chicken: Place the chicken breasts skin side down on a cutting board with the tenderloin folded back. Place 2 tablespoons of spinach filling on the center of the breast and fold the tenderloin over to enclose. Arrange the stuffed chicken breasts, skin side up, in a baking dish.
Mix the butter with the garlic, herbs, salt, and pepper. Rub the butter mixture over the chicken. Refrigerate for at least 15 minutes, until the butter hardens. Roast for 25 minutes. Let rest for 5 minutes, at room temperature, before serving. Slice chicken breasts and serve with pan juices.