Preheat the oven to 450 degrees F. Place four poblano peppers on a rimmed baking sheet and roasted in the oven for 15-20 minutes, until the skin is bubbly.
Meanwhile, heat a large skillet over medium heat. Add the butter to the skillet and once melted, add the hash browns. Liberally salt and pepper the hash browns, then brown for 5-8 minutes, stirring occasionally, until golden and crispy. Lower the heat to low.
In a medium bowl, whisk the eggs until frothy, then stir in the sun dried tomatoes, scallions, and Quesadilla Cheese. Pour the mixture over the hash browns and stir to combine. Cook the egg mixture for 2-3 minutes until just-under-cooked, but scoopable. Remove from heat.
Remove any loose skin from the top of the poblano peppers. Gently cut a slit in the top of each pepper and scoop out the seeds. Then spoon the egg mixture into the poblano peppers. Reshape the peppers with your hands.
Sprinkle Cotija cheese over the top of each pepper, and place back in the oven for 5-8 minutes, until the cheese is toasted and the eggs are cooked through.