Preheat the oven to 375°F Bake the bacon on a broiler pan until crisp, about 15 minutes.
While the bacon is working, trim and discard the crust from 1 slice of bread, then tear the slice into pieces. Arrange the rest of the bread on a baking sheet and lightly toast in the oven, about 5 minutes. Using a food processor, mix the lettuce, parsley, tarragon, mustard, lemon juice and torn bread. With the machine on, pour in 1/4 cup olive oil to form a thick sauce; season with salt and pepper.
In a large skillet, heat a drizzle of olive oil over medium-high heat or heat a grill pan and brush with olive oil. Add the chicken and cook, turning once, until golden, 4 to 6 minutes; season with salt and pepper.
Top each of 4 toasts with a chicken breast, 2 ham slices, 1 cheese slice (for melted cheese, broil the sammies for 1 minute), 2 tomato slices, salt, pepper and 2 bacon strips. Spread the lettuce puree on the remaining toasts and set on top. Slice the sammies into 4 triangles each.