In a large pot of boiling salted water, cook pasta, stirring occasionally, until al dente according to package directions. Reserve 1 cup pasta water before draining.
Meanwhile, season shrimp with ½ teaspoon salt and ¼ teaspoon pepper. In a large, high-sided skillet over medium-high heat, heat 2 tablespoons oil. Add shrimp and cook, turning halfway through, until just cooked through, 3 to 4 minutes. Transfer shrimp to a plate.
In same skillet over medium-high heat, heat remaining 1 tablespoon oil. Add bell pepper and cook, stirring occasionally, until just softened, about 3 minutes. Add scallions, garlic, and chopped jalapeño. Cook, stirring frequently, until fragrant, about 1 minute more.
Add reserved pasta water, chiles, adobo sauce, and tomato paste; season with salt. Bring to a simmer, stirring until combined. Slowly stir in cream, then add shrimp, pasta, and Parmesan. Cook over medium-high heat, tossing constantly, until sauce thickens and coats pasta, about 2 minutes more.
Divide pasta among plates. Top with more scallions and thinly sliced jalapeño.
