Heat a gas or charcoal grill to high heat. Brush the grill grates with oil.
For the pickled red onions: Bring the vinegar, 1/4 cup water, sugar and salt to a boil in a small saucepan. Remove from the heat and let cool for 10 minutes. Put the onions in a medium bowl, pour the vinegar over, cover and refrigerate for at least 4 hours and up to 48 hours before serving.
For the pickled jalapeno relish: Combine the jalapenos, pickles, cilantro, olive oil and salt and pepper to taste in a small bowl. Cover and let sit at room temperature for at least 15 minutes before serving.
For the chipotle ketchup: Stir together the ketchup and adobo sauce in a small bowl. Use right away or cover and refrigerate for at least 30 minutes to allow the flavors to meld. The sauce will keep for 1 week in a tightly sealed container in the refrigerator.
For the burgers: Divide the meat into 4 equal portions (about 6 ounces each). Shape each portion with your hands into a round patty, about 3/4 inches thick. Use your thumb to make a divot in the center of each burger. Sprinkle both sides of each burger with salt and pepper.
Grill, covered, until golden brown and slightly charred on the first side, 3 to 4 minutes. Flip the burgers and cook until golden brown and slightly charred on the second side, about 4 minutes for medium.
While the burgers cook, toast the buns on the grill until lightly charred, 10 to 15 seconds. Set aside.
Add 2 slices of cheese to the tops of each burger. Cover the burgers with the grill lid, large domed lid or large metal bowl and count to 10 until the cheese is melted.
Place the burgers on the bottom buns. Top with the chipotle ketchup, pickled jalapeno relish, pickled red onions, avocado and the top buns and serve immediately.