Roast the Brussels Sprouts:
Preheat your oven to 425°F (220°C). Toss the halved Brussels sprouts with extra virgin olive oil and a pinch of salt. Spread them cut side down on a baking sheet and roast for 20–25 minutes until golden and caramelized. Set aside.

Cook the Pasta:
Bring a large pot of salted water to a boil. Cook the pasta shells until al dente according to package directions. Reserve 1 cup of pasta water, then drain and set aside.

Crisp the Prosciutto:
While the pasta cooks, heat a large skillet over medium heat. Add prosciutto slices and cook 2–3 minutes per side until crisp. Transfer to a paper towel-lined plate to cool, then crumble into shards.

Brown the Butter:
In a large skillet, melt the butter over medium heat. Cook, swirling occasionally, until it foams and turns nutty brown, about 3–4 minutes.

Stir in Miso and Garlic:
Reduce the heat to low. Add the garlic and miso paste to the browned butter, stirring until the garlic softens and the miso dissolves completely, about 2 minutes.

Make the Egg Mixture:
In a small bowl, whisk together the egg, egg yolks, Parmesan, and black pepper until smooth.

Combine Pasta and Sauce:
Remove the skillet from heat. Add the drained pasta and roasted Brussels sprouts to the miso-butter mixture and toss to coat evenly.

Stir in Egg Mixture:
Slowly drizzle the egg mixture into the skillet, stirring constantly to create a glossy, creamy sauce. Add reserved pasta water a splash at a time until the sauce is silky and clings to the pasta.

Serve:
Taste and adjust salt as needed. Plate the pasta and top with crispy prosciutto shards and extra Parmesan. Serve hot.