Grill or dry toast the bread until light golden brown on both sides. Trim a small chunk off the end of a garlic clove and rub the cut surface all over the toasted bread (the garlic will wear down as you rub the bread).
Bring a pot of water to a boil. Score the skin of the tomatoes with a small x using a paring knife. Blanch the tomatoes in the boiling water for 30 seconds, then drop them into a bowl of ice water. Peel the tomatoes, halve them and then squeeze the seeds out. Chop the tomatoes into small dice and mix in a bowl with the parsley, chives, anchovy if using, shallots and a splash of sherry vinegar. Season generously with salt and pepper, and drizzle with olive oil to taste. Set aside.
Slice the Serrano or Iberico ham into thin slices, leaving the fat on. Heat a large nonstick fry pan over medium heat. Add 1 tablespoon olive oil and then the ham slices. Allow the ham to render for 15 to 20 seconds, turning the slices occasionally. Remove from the pan to a plate and keep the rendered fat in the pan.
Turn the heat up to medium-high and add the asparagus pieces to the pan. Season the asparagus with salt and pepper and saute until tender and the asparagus begins to color slightly, 1 to 2 minutes. Remove the asparagus to the plate with the ham.
Fry the eggs sunny-side up in the same pan (add olive oil to the pan if necessary).
To assemble, drain some of the liquid off the tomato salsa. Smear each toast with a good amount of tomato salsa. Place the ham and then the asparagus spears on the toast next. Then top off with a trimmed sunny-side up egg. Sprinkle with smoked paprika, salt and pepper, then drizzle with olive oil. Serve immediately.