Preheat the broiler. Place the tomatillos, poblanos and whole jalapeno on a rimmed baking sheet and broil, turning occasionally, until charred and softened, 18 to 20 minutes. (Turn the oven temperature to 375 degrees F.) Set aside until cool enough to handle. Peel the skin from the poblanos and remove the seeds. Transfer the flesh to a blender, along with the tomatillos, jalapeno and any accumulated juices. Add the chopped cilantro, juice of 3 limes and salt and pepper to taste. Blend until smooth, then set aside.
In a medium pot over high heat, warm the olive oil until shimmering. Add the beef, sprinkle generously with salt and pepper, and cook until nearly cooked through, about 5 minutes. Set aside 1/3 cup onion for serving, then add the remaining onion and the garlic to the beef and continue to cook, stirring, until golden in spots, about 8 minutes more. Add the cumin and cook, 30 seconds. Add the tomatillo mixture to the pot and stir to combine. Season to taste with salt and pepper. Keep warm.
Place a third of the chips on an oven-safe baking sheet or platter. Sprinkle with a third of the cheese. Layer on the remaining chips and cheese in the same manner, creating 3 layers of evenly-distributed chips and cheese. Transfer to the oven and bake until the cheese is melted and bubbling, about 8 minutes. Meanwhile, mash the avocado with the remaining lime juice and season to taste with salt and pepper.
Top the hot nachos with spoonfuls of warm tomatillo-beef mixture, mashed avocado, sour cream, sliced jalapenos, pepitas, reserved 1/3 cup diced red onion and reserved cilantro sprigs. Serve immediately.