In a medium bowl, flake the tuna finely with a fork. Add the celery, scallions, and dill, and continue mixing and fluffing with the fork until combined. Add the lemon juice, 1 1/2 teaspoons salt, and 3/4 teaspoon pepper. Combine the mayonnaise and anchovy paste, if using, and mix into the tuna.
Preheat the broiler. Toast the bread in a toaster and place the slices in a single layer on a sheet pan. Spread a quarter of the tuna mixture thickly and evenly on each piece of bread, covering the entire slice. Sprinkle the cheese evenly on the 4 sandwiches, covering the tuna completely. Broil for 1 to 2 minutes, just until the cheese melts and starts to brown. (Watch it carefully!) Sprinkle with the microgreens and serve hot.