PICKLED RED ONION: Peel and slice red onion into thin rounds. (A mandolin may be helpful.) Place in a glass bowl or jar.
In a small pot, combine vinegar, sugar, and salt. Bring to a boil. Pour over onion and let sit, stirring occasionally. (The rings will break up and separate.) When mixture reaches room temperature, cover and refrigerate. Let sit overnight, or until onion rings are soft and pink.
SANDWICH: Cut ciabatta into ½-inch slices. Slice mozzarella into ¼- to ½-inch circles. Cut pan de orejon into ¼-inch slices. Remove a few spoonfuls of pickled red onion from liquid and drain on paper towels while preparing remaining ingredients.
Arrange 6 pairs of bread slices, side by side. On one, place a circle or two of mozzarella, and season with salt and pepper. Top with a slice or two of the apricot cake, and then with pickled onion. Top with another slice or two of mozzarella, and season again with salt and pepper. Top with second slice of bread. Drizzle or brush bread with olive oil.
Heat a dry skillet over medium heat. Place sandwiches in pan, oil side down, and cover with a lid. Toast until golden brown. Brush or drizzle the second side with oil and flip. Cover and toast other side, until browned. Remove, slice, and serve immediately.