Pre-heat your oven to 350 degrees. Line 2 large baking sheets with parchment and briefly set aside.
Using the large holes of a box grater, grate the Président Manchego. Pour a tablespoon of the grated Manchego onto the prepared baking sheet and pat it down so that the cheese is in a thin round (about 2½-inches in diameter) . Repeat with the remaining cheese, making sure to leave about an inch between each round. Sprinkle the rounds with a generous amount of coarse black pepper.
Bake for 8 minutes until the cheese turns a deep golden brown. Remove from the oven and let cool for 5 minutes on the baking sheets, then use a spatula to loosen the crisps from the parchment and transfer them to a wire rack to cool completely.
Meanwhile, tear the Serrano ham into 2-inch pieces. Slice the brie into 1-inch slices, cut the quince paste into very small cubes, and chop the Marcona almonds.
Top each Manchego Crisp with a slice of Brie, a couple pieces of Serrano ham, a few quince cubes, and a sprinkling of chopped almonds. Serve immediately.