01 - Preheat oven to 400°F. Slice the top off the garlic head to expose the cloves. Drizzle with olive oil and season with a pinch of salt. Wrap tightly in aluminum foil and roast for 30–35 minutes until the cloves are soft and deeply golden. Remove from the oven, let cool slightly, then squeeze the roasted cloves out of their skins into a small bowl and mash into a smooth paste.
02 - Heat neutral oil in a small saucepan over medium heat until shimmering. 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 a paper towel-lined plate and immediately sprinkle with salt. Set aside.
03 - Bring a large pot of generously salted water to a rolling boil. Add the radiatori and cook 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 unsalted butter. Continue cooking, stirring constantly with a whisk or spoon, until the butter foams and then turns a deep golden brown with a fragrant nutty aroma, about 3–4 minutes. Watch carefully to avoid burning.
05 - Reduce heat to low. Add the miso paste and mashed roasted garlic to the brown butter, whisking vigorously until the miso dissolves completely and the mixture is smooth and emulsified.
06 - Add the drained pasta to the skillet and toss well to coat every piece. Sprinkle in the Parmesan cheese and add a splash of the reserved pasta water, stirring continuously until a glossy, silky sauce clings to the pasta. Add lemon juice if using, then season generously with black pepper. Adjust consistency with additional pasta water as needed.
07 - Divide the pasta among warmed plates or bowls. Finish each portion with a generous mound of crispy shallots, an extra shower of Parmesan, and a scattering of fresh herbs if desired. Serve immediately.