Position racks in the upper third and middle of the oven; preheat the broiler. Whisk the vinegar and sugar in a small bowl until dissolved. Stir in the red onion and set aside.
Put the potatoes in a medium saucepan and cover with cold water by 1 inch; season with salt. Bring to a boil and cook until the potatoes are tender, 12 to 15 minutes.
Meanwhile, toss the shishitos and asparagus with 1 tablespoon olive oil and a big pinch each of salt and pepper on a baking sheet.
Drain the potatoes and toss with 2 tablespoons olive oil and the paprika; season with salt and pepper. Spread out on a second baking sheet and smash the potatoes using the bottom of a glass. Broil the potatoes on the upper oven rack and the shishitos and asparagus on the middle rack until the potatoes are browned and the shishitos and asparagus are tender, 10 minutes.
Meanwhile, cook the chorizo in the remaining 1 tablespoon olive oil in a nonstick skillet over medium-high heat until browned, 5 minutes. Remove to a plate. Add 4 eggs to the skillet and cook until the whites are set, 3 to 4 minutes; season with salt and pepper. Divide the potatoes, shishitos and asparagus among plates. Top with the chorizo, red onion (drained) and fried eggs. Sprinkle with the parsley and paprika.