Step 1

Preheat oven to 350°F. Toss together potatoes, 2 tablespoons oil, and 1 teaspoon salt on a rimmed baking sheet, and spread in a single layer. Bake in preheated oven until fork-tender, 30 to 40 minutes. Remove from oven.

Step 2

Increase oven temperature to 500°F. Using the bottom of a 1-cup dry measuring cup, smash potatoes to about 1/2-inch thickness. (Make sure smashed potatoes are still in a single layer.) Drizzle with 3 tablespoons oil; sprinkle with 1 teaspoon salt. Bake at 500°F until bottoms of potatoes are golden brown, 15 to 20 minutes. Flip potatoes, drizzle with remaining 1 tablespoon oil, and sprinkle with 1/4 teaspoon salt. Bake until edges of potatoes are crispy and golden, 8 to 12 minutes.

Step 3

While potatoes bake, process onion, 1/3 cup water, serrano, 3 tablespoons cilantro, lime juice, and remaining 11/4 teaspoons salt in a blender until smooth, about 20 seconds. Add avocado, and process until smooth, about 10 seconds. If needed, pulse in additional cold water, 1 tablespoon at a time, to reach a thick but pourable consistency.

Step 4

Transfer warm potatoes to a large bowl; add pickled jalapeño slices and pickling liquid, Cotija, and 1/2 cup cilantro; toss to coat. Spoon avocado salsa into 4 small bowls; top evenly with potato mixture, and sprinkle with remaining 1 tablespoon cilantro. Serve immediately.