Trim any excess fat off of the chicken breasts and place them on a large plate. Set aside.
Place a large piece of plastic wrap on a flat, dry surface and place two of the chicken breasts, smooth side up, on top. Then add another large piece of plastic wrap on top of the chicken. Use the smooth side of a meat mallet, or the bottom of a small sauté pan to pound the chicken until it's evenly flattened, about ¼ to ½-inch thick. Repeat this with the remaining two chicken breasts.
Turn the chicken breasts over, so the rough side is up, and they are laying vertically in front of you, and season the surface of each one with salt and pepper.
In a single layer, cover the surface with spinach leaves, and gently press them down. (Amounts will vary depending on the size of your chicken breasts and how thinly you've pounded them.)
Now add about 2 tablespoons of the Gruyère evenly over the spinach.
Beginning with the end closest to you, roll the chicken tightly, and evenly, away from you. Then place the roll on a new, clean piece of plastic wrap and wrap it very tightly. Repeat this with the remaining three chicken breasts, and refrigerate them for at least 1 hour.
While the chicken is refrigerating, mix the hazelnut meal, paprika and salt in a shallow bowl.
Lightly beat the egg in another shallow bowl.
Coat the bottom of a large sauté pan with olive oil and place it over medium-high heat.
Unwrap each chicken roll and carefully dip it in the blended egg, being sure it's evenly coated. Then gently press it into the hazelnut meal mixture, on all sides. Do this a couple of times so that you have a nice thick layer which uses about ¼ of the mixture for each roll.
Once the pan is very hot, add the well-coated chicken rolls. You should hear a sizzling sound when they hit the pan -- if you don't it's not hot enough yet. Brown the bottom and top very well, about 2 minutes each. Then turn the heat to low, cover the pan, and cook until the chicken cooked through, about 15 minutes. (It's easiest to use kitchen tongs to turn the chicken.)
Let them sit for about 5 minutes and then serve. (For a pretty presentation, slice them and serve over sautéed spinach with roasted hazelnuts.)