Preheat the oven to 375 degrees F. Cook the bacon in a skillet over medium heat, turning, until very crisp. Drain on paper towels until cool, then finely chop.
Stir the bacon, 1/2 cup parmigiano-reggiano and the flour in a small bowl. Line a baking sheet with a silicone mat or parchment paper. Divide the bacon-cheese mixture into 4 mounds on the baking sheet and flatten each one into about a 3 1/2-inch round. Bake until golden brown and the cheese melts, about 7 minutes. Let cool on the baking sheet 5 minutes, then carefully transfer to a rack using a thin spatula and let cool completely.
Make the dressing: Whisk the anchovies, garlic, lemon juice, olive oil, Worcestershire sauce and the remaining 3 tablespoons cheese in a small bowl.
Arrange the tomatoes on a platter, sprinkling each layer with salt, pepper and some of the dressing. Scatter the watercress on top and drizzle with olive oil. Break the bacon-parmesan crisps into bite-size pieces and add to the salad.