Pre-heat the oven to 375°F.
Combine the dressing ingredients in a bowl and reserve.
Heat a griddle (or flat side of a grill pan) or large, nonstick skillet over medium-high heat.
Arrange the bacon on a slotted broiler pan or metal wire rack set atop a rimmed baking sheet and bake to crisp, 15-18 minutes.
Season the tomatoes and sliced onions with salt and pepper, separate lettuce leaves, a couple for each sandwich. Douse the sliced avocado with lemon juice to keep from browning and to add acidity to the buttery flavor.
Dress the chicken cutlets with oil and season with salt and pepper. Grill or griddle to golden on each side, about 6-7 minutes total, turning once. Remove and wipe off the griddle, then reduce the heat to medium-low, add a pat of butter and melt. Brown the rolls cut-side down; remove. Add a pat more of butter and melt; fry the eggs to medium-over doneness. Season the eggs with salt and pepper.
Pile up the Cobbwiches: bun bottom, dressing, B, L, T, O, A, chicken, egg, bun top. Serve it up!