Slice chicken breasts lengthwise into 1/2-inch thick strips.
In a shallow bowl, whisk flour with paprika, garlic powder, onion powder, salt, and pepper.
In another bowl, whisk egg and 1/2 cup buttermilk.
Heat about 1/2 inch oil in a large skillet over medium-high heat until shimmering (350°F).
Dip each chicken strip into egg mixture, then dredge in flour mixture, shaking off excess.
Fry in batches without crowding, 3-4 minutes per side until golden and cooked through (internal temp 165°F). Drain on paper towels.
Meanwhile, make dressing: whisk mayonnaise, 1/4 cup buttermilk, lemon juice, 1/2 teaspoon garlic powder, dill, and salt and pepper until smooth.
In a large bowl, toss greens, tomatoes, cucumber, onion, and feta with dressing.
Divide salad among plates, top with warm fried chicken strips, and serve immediately.