Turn on the broiler and adjust the rack so that it’s about 4 inches below heat. Lay the poblanos and garlic on a baking sheet and roast, turning occasionally, until they have softened and blackened in spots, about 10 minutes for the chiles and 15 for the garlic. Set aside to cool.
Meanwhile, prepare the squash: Slice through the squash widthwise, separating the rounded bottom from the skinnier “neck”; reserve the bottom for another use. Cut the neck in half lengthwise and, using a mandolin, slice each half into thin, 1/8-inch-thick sheets. Slice the sheets lengthwise into ¼-inch-wide strips. You should have about 2 cups of butternut “pasta.”
Peel the poblanos, pull out the stems and seed pods, then quickly rinse to remove stray seeds and bits of skin. Cut 1 poblano into ¼-inch strips to match the butternut; roughly chop the other 2 poblanos and scoop into a blender.
Warm the cream (or one of its stand-ins) in a glass measuring cup in a microwave for 1 minute at half-power. Pour into the blender jar with the poblanos. Peel the garlic, roughly chop, add to the blender and blend until completely smooth. Taste and season with salt (usually about a teaspoon). Pour into a large (10-inch) skillet set over low heat.
In a large (8-quart) saucepan, bring 6 quarts water and 2 tablespoons salt to a boil. Drop in the squash strips and cook until al dente, 1 to 2 minutes. Remove with a slotted spoon, shaking off the excess water, and add to the skillet with the poblano cream. Add the fettuccine to the boiling water and cook until al dente, 10 to 12 minutes. Drain, reserving ¼ cup pasta water. Add the pasta, reserved water and poblano strips to the sauce. Turn the heat to medium-high and bring the sauce to a simmer, all the while tossing the pasta, squash and poblanos together. Stir in ½ cup of the queso and divide the pasta among four bowls. Divide the remaining ½ cup of the queso among the bowls, and sprinkle each one with cilantro.