Combine all the romesco ingredients in a food processor or blender. Pulse until the mixture is pasty and still a little chunky.
In a bowl, add the asparagus and drizzle it with olive oil. Sprinkle with salt and pepper. Toss to combine. Transfer the asparagus to the grill and cook for about 10-12 minutes or until the asparagus is slightly tender and charred edges have formed.
Transfer the asparagus to a serving platter. Top with cheese and chopped almonds if desired.