Preheat oven to 375°F.
Combine dressing ingredients in a bowl and reserve.
Heat a griddle (flat side of grill pan) or large, nonstick skillet over medium-high heat.
Arrange bacon on a slotted broiler pan or metal wire rack set atop a rimmed baking sheet and bake to crisp, 15-18 minutes.
Season 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 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 griddle, reduce heat to medium-low add a pat of butter and melt. Brown rolls cut-side down; remove. Add a pat more of butter and melt, fry eggs to medium-over doneness. Season eggs with salt and pepper.
Pile up the Cobbwiches: bun bottom, dressing, B, L, T, O, A, chicken, egg, bun top. Serve it UP!