Preheat a panini press or place a large skillet over medium-high heat.
In the bowl of a food processor, puree the pimientos and piquillo peppers. Spread the puree onto the slices of bread and scatter some parsley leaves over each slice.
Lay down a slice of cheese on four of the slices, top each with a few slices of Serrano and another slice of cheese and then cap them off.
Place the sandwiches in the press or skillet and grill until toasted and heated through (if using the skillet, weigh the sandwich down with another pan and flip it over once one side is toasted).
Cut the sandwiches up and serve.