Preheat your grill to medium-high heat.
In a large bowl, combine the ground beef, garlic powder, onion powder, smoked paprika, salt, and pepper. Mix until just combined, then form into 4 equal patties.
Lightly coat the poblano peppers with cooking oil and place them on the grill. Grill for about 10-12 minutes, turning occasionally, until the skin is charred and blistered. Remove from the grill, place in a bowl, and cover with plastic wrap to steam for about 10 minutes. Once cooled, peel off the charred skin, remove the seeds, and slice them open.
In a small bowl, mix the cream cheese, cheddar cheese, cilantro, and lime juice until well combined.
Grill the burger patties for about 4-5 minutes on each side for medium doneness. During the last minute of cooking, place a slice of pepper jack cheese on each patty to melt.
To assemble the burgers, spread a generous amount of the cream cheese mixture on the bottom half of each bun. Place the grilled burger patty on top, followed by the grilled poblano pepper and avocado slices. Top with the other half of the bun and serve immediately.