Heat the oven to 350°F. Heat 2 teaspoons of the oil in a large frying pan over medium heat until shimmering. Add onion and sauté until soft, about 8 to 10 minutes. Add spinach and sauté until wilted and water evaporates, about 2 minutes. Add nutmeg and season with salt and freshly ground black pepper. Remove mixture from the pan and transfer to a bowl to cool. Wipe out the pan and set aside.
Cut each chicken breast in half horizontally. Using a mallet or the bottom of a pan, pound chicken pieces to an even thickness, about 1/4 inch thick. Season all over with salt and freshly ground black pepper.
Stir feta into cooled spinach mixture. Lay chicken breasts on a cutting board so the narrowest ends face you. Place 1/4 of the spinach mixture halfway up each chicken piece. Fold the bottom of the chicken up over the filling to enclose it, then roll into a tight cylinder. Use toothpicks or butcher’s twine to secure the rolls. Repeat with remaining chicken and filling.
Return the frying pan to medium-high heat and add remaining 1 tablespoon olive oil. Once oil is shimmering, place chicken breasts in the pan and cook undisturbed until golden brown, about 4 to 6 minutes. Turn breasts over and transfer the pan to the oven. Bake until the filling is hot and the interior of the chicken rolls is white but still juicy, about 8 minutes.
Variations: Stir in 1/4 cup of either pine nuts, currants, or a combination when adding the feta to the spinach mixture.
Beverage pairing:Markus Huber Grüner Veltliner “Hugo,” Austria. A white with sharpness, a hint of bitterness, and some tang is called for, and this Grüner Veltliner fits the bill, echoing the spinach and feta while resonating with the chicken.