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 deeply softened 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 the 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, stirring gently, until the butter becomes foamy 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 brown butter, whisking vigorously until the miso is fully dissolved and the mixture is smooth and emulsified.
06 - Add the drained pasta to the skillet and toss thoroughly to coat every piece. Sprinkle in the Parmesan along with a splash of the reserved pasta water, stirring continuously to create a glossy, clinging 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 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.