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