1. CUT AND BRINE Cut each chicken breast diagonally into thirds, then cut each third diagonally into ½-inch-thick pieces. Whisk water, tablespoon salt, and Worcestershire in large bowl until salt dissolves. Add chicken pieces and refrigerate, covered, for 30 minutes.
2. COAT CHICKEN Remove chicken from brine, discard brine, and pat chicken dry with paper towels. Combine flour, bread crumbs, onion powder, remaining salt, pepper, garlic powder, and baking soda in shallow dish. Whisk egg whites in second shallow dish until foamy. Coat half of chicken with egg whites and dredge in flour-crumb mixture, pressing gently to adhere. Transfer to plate and repeat with remaining chicken (don’t discard flour-crumb mixture). Let sit 10 minutes.
3. FRY Adjust oven rack to middle position and heat oven to 200 degrees. Heat oil in large Dutch oven over medium-high heat to 350 degrees. Return chicken to flour dish and turn to coat, pressing flour-crumb mixture gently to adhere. Fry half of chicken until deep golden brown, about 3 minutes, turning halfway through cooking. Drain chicken on wire rack set inside rimmed baking sheet and place in oven. Return oil to 350 degrees and repeat with remaining chicken. Serve with dipping sauces (see related recipes.)
MAKE AHEAD: Cool fried nuggets, transfer to zipper-lock bag, and freeze for up to 1 month. To serve, adjust oven rack to middle position and heat oven to 350 degrees. Place nuggets on rimmed baking sheet and bake, flipping once, until heated through, about 15 minutes.