Preheat a grill or broiler to high. Grill the red peppers, turning often with tongs, until blistered and blackened on all sides, about 15 minutes. Alternatively, roast the peppers directly over the stovetop flame of a gas oven. Transfer to a large bowl, cover with plastic wrap, and let steam for 20 minutes. Peel the peppers and chop them into ½-inch pieces.
Heat the olive oil in a large skillet over medium-high heat. Add the anchovies and garlic and cook for 1 minute. Stir in the chopped red peppers, then add the white wine. Boil until the pan is nearly dry. Stir in the kale and chili flakes. Remove from the heat.
Bring a large pot of water to a boil, add salt, and drop in the pasta. Cook for about 9 minutes or until the pasta is tender. You will be cooking it further in the sauce. Drain, reserving some of the pasta water. Return the sauce to medium-high heat and stir in the pasta. Cook for 5 minutes, to allow the flavours to mingle. Add a spoonful of pasta water if the sauce looks too dry. Remove from the heat.
Season with salt and pepper. Add the pine nuts and parsley and toss well. Tip into a large serving bowl, garnish with an over-generous grating of Parmigiano-Reggiano, and serve immediately.