Preheat your grill or broiler to lightly roast the jalapeños until their skins are charred and bubbly, about 4-5 minutes per side. Once cooled, remove the stems, seeds, and roughly chop them. Set aside.
In a medium saucepan, melt the butter over medium heat. Add the flour and whisk constantly for about 1 minute, creating a smooth, slightly bubbly roux without browning.
Gradually pour in the milk while whisking to prevent lumps. Continue stirring until the mixture thickens, about 3-4 minutes, and has a creamy, smooth consistency.
Add the shredded cheese in handfuls, stirring gently until each addition melts completely into the sauce, resulting in a glossy, velvety texture.
Stir in the roasted jalapeños, ancho chili powder, and lime zest, blending everything together evenly. Season with salt and pepper to taste, and cook for another 2 minutes to meld flavors.
Remove the saucepan from heat and transfer the dip to a serving bowl. The dip should be hot, bubbling slightly around the edges, with a smooth, creamy consistency.
Serve the dip warm, accompanied by tortilla chips, veggie sticks, or bread for dipping. Enjoy the smoky, cheesy, zesty flavors in every bite.
