Lightly beat the eggs, mustard, 1 teaspoon orange zest, ½ teaspoon salt, and ¼ teaspoon pepper together in a shallow dish. Mix the almonds and panko in a separate shallow dish. Working with one piece of chicken at a time, dip the chicken into the egg mixture using tongs, turning to coat well and allowing excess to drip off. Drop the chicken into the nut mixture and press the nuts into the chicken with your fingers. Transfer the breaded chicken to a wire rack set over a baking sheet and repeat with the remaining chicken. Adjust an oven rack to the middle position and heat the oven to 200 degrees.
Heat 6 tablespoons oil in a heavy-bottomed, 12-inch nonstick skillet over medium-high heat until just smoking. Place the chicken in the skillet gently and cook until golden brown and crisp on the first side, about 2½ minutes. Using tongs, flip the chicken; reduce the heat to medium and continue to cook until the meat feels firm when pressed gently, the second side is deep golden brown and crisp, and the chicken is no longer pink in the center, about 2 minutes longer. Transfer the chicken to a paper towel-lined plate and place the plate in the oven. Discard the oil in the skillet and, using tongs and paper towels, wipe the skillet clean.
Place the spinach in a large bowl. Heat 1 tablespoon oil in the cleaned skillet over high heat until just smoking. Add the orange slices and cook until lightly browned around the edges, 1½ to 2 minutes. Remove the pan from the heat and add remaining 1 tablespoon oil, shallot, remaining ¼ teaspoon zest, ¼ teaspoon salt, and 1/8 teaspoon pepper and allow residual heat to soften the shallot, 30 seconds. Pour the warm dressing with the oranges over the spinach and toss gently to wilt. Remove the chicken from the oven and serve it immediately with the salad and orange wedges.