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 30–35 minutes until the cloves are soft and caramelized. Let cool, then squeeze the roasted cloves out of 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 3–5 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 radiatori according to package directions until al dente. Reserve 1 cup of starchy pasta water before draining.
04 - In a large skillet, melt the unsalted butter over medium heat. Continue cooking, stirring gently and watching closely, until the butter foams and turns a deep golden brown with a fragrant nutty aroma, about 3–4 minutes.
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 to coat evenly. Sprinkle in the Parmesan cheese along with a splash of reserved pasta water, stirring continuously to form 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 warmed plates. Finish each portion with crispy shallots, a generous shower of extra Parmesan, and a scattering of fresh herbs if desired. Serve immediately.