Bring a large pot of salted water to a boil. Heat the olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Add the scallions, snap peas, jalapeno and 1/4 teaspoon salt and cook, stirring, until soft, about 4 minutes. Transfer to a serving bowl and toss with the parsley and chives; reserve the skillet.
Meanwhile, cook the pappardelle in the boiling water until al dente, about 6 minutes. Reserve 2/3 cup of the cooking water, then drain the pasta and toss with the vegetables.
Pour the reserved cooking water into the skillet and add the remaining 2 tablespoons butter. Bring to a boil, whisking until the butter melts, then cook until reduced slightly, about 2 minutes. Pour the sauce over the pasta, sprinkle with 1/2 cup cheese and toss. Top with the remaining 1/4 cup cheese.