Prepare the Tomato Pulp: Cut the Roma tomatoes in half crosswise. Press the cut side of each tomato half against the large holes of a box grater set over a medium bowl. Grate firmly until only the tomato skin is left in your hand; discard the skins. To the resulting tomato pulp, stir in the sherry vinegar, fine sea salt, and black pepper. Set aside to allow the flavors to meld.
Prepare the Bread: Arrange the four slices of whole-grain sourdough on a cutting board. Using a pastry brush or your fingertips, brush approximately 1 tablespoon of the extra virgin olive oil evenly over one side of each bread slice.
Toast the Bread: Place a large cast-iron skillet over medium-high heat. Once the skillet is hot, place the bread slices oiled-side down. Sear for 2-3 minutes, or until the undersides are golden brown with distinct char marks. Flip the bread and toast the second side for another 1-2 minutes until crisp.
Infuse with Garlic: Immediately remove the hot, toasted bread from the skillet and place it on a serving platter. Take the halved garlic clove and firmly rub its cut surface over the top, craggy side of each hot slice. The heat from the bread will release its aromatic oils.
Assemble the Toasts: Give the tomato pulp a final stir. Spoon the mixture generously over the garlic-rubbed surface of each bread slice, spreading it evenly to the edges.
Garnish and Serve: Drizzle the remaining ½ tablespoon of extra virgin olive oil over the four prepared toasts. Garnish with a sprinkle of finely chopped fresh oregano and a light dusting of smoked sweet paprika. Serve immediately for the best texture and flavor.