Cook bell pepper, onion, garlic and broccoli slightly in 1 t butter.
In a large bowl, toss together chicken, broccoli, red bell pepper, garlic, Cheddar cheese, mayonnaise, dill weed, salt, almonds and onion.
Unroll crescent roll dough, and arrange flat on a medium baking sheet with parchment paper. Pinch together perforations to form a single sheet of dough. Using a knife or scissors, cut 1 inch wide strips in towards the center, starting on the long sides. There should be a solid strip about 3 inches wide down the center, with the cut strips forming a fringe down each side. Spread the chicken mixture along the center strip. Fold the side strips over chicken mixture, alternating strips from each side. Pinch or twist to seal.
Brush braided dough with the egg white. Bake in the preheated oven 25 to 28 minutes, or until golden brown.