01 - Preheat oven to 400°F. Slice the top off the garlic head to expose the cloves. Drizzle with olive oil, sprinkle with a pinch of salt, wrap tightly in aluminum foil, and roast for 30 to 35 minutes until cloves are deeply soft and golden. Let cool, then squeeze the roasted cloves into a bowl and mash into a smooth paste.
02 - Heat neutral oil in a small saucepan over medium heat. Add thinly sliced shallots in small batches and fry, stirring frequently, until golden brown and crisp, about 3 to 5 minutes per batch. Transfer with a slotted spoon to paper towels to drain and immediately sprinkle with salt. Set aside.
03 - Bring a large pot of generously salted water to a rolling boil. Cook the radiatori according to package directions until al dente. Reserve 1 cup of starchy pasta water before draining.
04 - In a large skillet, melt the butter over medium heat. Continue cooking, swirling the pan occasionally, until the butter foams and turns a deep golden brown with a fragrant nutty aroma, about 3 to 4 minutes. Watch carefully to prevent burning.
05 - Reduce heat to low. Add the miso paste and mashed roasted garlic to the brown butter, whisking vigorously until fully incorporated and smooth.
06 - Add the drained pasta to the skillet and toss thoroughly to coat every piece. Sprinkle in the Parmesan cheese along with a splash of the reserved pasta water, stirring until a glossy, silky sauce clings to the pasta. Add lemon juice if using. Season generously with black pepper and adjust consistency with additional pasta water as needed.
07 - Divide the pasta among warmed plates or bowls. Finish each portion with a generous handful of crispy shallots, an extra shower of Parmesan, and a scattering of fresh herbs if desired. Serve immediately.