Make the pickled onions: Heat vinegar, wine and sugar in a small saucepan, stirring until sugar is dissolved. Bring to a boil, remove from heat and pour over onions in a medium bowl. Cool the onions and the liquid in an ice bath. Make at least 2 hours ahead of time needed.
Make the green chile salsa: Heat grill to medium-high heat, then char green chiles and poblano pepper. Remove from heat and, when cool enough to handle, peel skin (you may want to wear gloves when handling the peppers). Split chiles and remove seeds. Cut tomatillos in half and drizzle with olive oil and 1/4 teaspoon of salt, then char on the grill until medium in color. In a food processor, blend the chiles, tomatillos, lime juice and remaining 3/4 teaspoon salt. Fold in the cilantro. Taste and add additional if needed. Chill until ready to serve.
Make the burgers:Heat grill to medium heat. Season each burger patty with salt and black pepper. Grill burgers approximately 4 minutes on each side for medium-rare, or until desired doneness. Remove from heat. Top burgers with the queso fresco.
Lightly toast buns over the grill. Place shredded lettuce on each bun, place a burger on top of lettuce, spoon green chile salsa over each burger, top each burger with a quarter of the avocado and pickled red onions. Enjoy!