Make the dressing:

In a medium bowl or liquid measuring cup, combine the buttermilk, sour cream, vinegar, and honey. Slowly whisk in the oil to blend. Stir in the chives and season to taste with salt and pepper.

Cook the chicken:

Lightly beat the eggs in a wide, shallow dish. Pulse the almonds and flour together in a food processor until the almonds are chopped; transfer the almond mixture to another wide, shallow dish. Season the chicken on all sides with 1 tsp. salt and 3/4 tsp. pepper. Dip one piece of chicken at a time in the eggs. Shake off the excess and dredge in the almond mixture, pressing lightly to help it adhere. Set aside on a wire rack.

Heat 2 Tbs. of the oil in a large skillet over medium heat until shimmering hot. Working in batches, cook the chicken until light golden brown on both sides and just cooked through, 3 to 4 minutes per side. Transfer the chicken to a paper-towel-lined plate when done. Between batches, remove any stray almonds from the pan and add more oil if necessary.

Assemble the salad:

In a large bowl, toss the lettuce, arugula, or both and the nectarines with about half of the dressing. Season to taste with salt and pepper. Divide among 4 dinner plates. Divide the chicken among the plates, overlapping the pieces on top of the salad. Drizzle additional dressing over the chicken and serve.