Char the peppers on all sides by places over the flame of a gas stove burner (this will not work on the coils of an electric stove, or an induction burner). If you don’t have a gas burner, add the peppers to a baking sheet and place them just under the broiler in your oven. Turn the peppers until charred on all sides, remove from heat, allow to cool.
Heat the oven to 375°F.
Heat the olive oil in a large skillet, then add the chicken cooking until seared on all sides.
Add the beer, scraping to deglaze the pan. Add the cream cheese, ½ cup mozzarella, paprika, garlic powder, chili powder, and salt. Stir until cheese is melted and well combined.
Stir in the tomatoes.
Add to a baking sheet, cut the peppers down the center from the stem to the tip, removing the seeds and membrane.
Fill the peppers with the chicken mixture. Sprinkle with the remaining mozzarella cheese.
Bake until the cheese has melted, about 10 minutes, remove from oven.
Stir together all the elote ingredients, set aside.
Add all the avocado sauce ingredients to a food processor, process until well combined but the avocado is still slightly chunky.
Plate the peppers, top with elote and avocado sauce.