Put the almonds in a mini-chopper or food processor and pulse until finely chopped. Transfer to a shallow dish and stir in the pimenton. Lightly whisk the egg whites in another shallow dish. Pat the chicken dry and season both sides with salt and pepper. Dip the chicken into the egg white and shake off any excess. Dredge the chicken in the almonds to coat. Place on a baking sheet, cover and refrigerate for 20 minutes.
Set a wire rack on a baking sheet. Heat a medium nonstick skillet over medium-low heat and add the butter and 1 tablespoon of the oil. Place the chicken smooth-side down in the pan and increase the heat to medium-high. Cook, turning once, until a golden brown crust forms, 3 to 4 minutes per side. Transfer the chicken to the prepared baking sheet and bake until an instant-read thermometer inserted into the thickest part of the chicken registers 160 degrees F, about 20 minutes.
Whisk together the vinegar and salt and pepper to taste in a medium bowl. Gradually whisk in the remaining 3 tablespoons olive oil. Add the salad greens and toss to coat. Divide the salad evenly among 4 plates and serve with a piece of chicken.
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