Add marjoram sprig to a large pot of salted water; bring water to a boil.

Meanwhile, cut asparagus stems crosswise into 1/4-inch-thick pieces, reserving tips.

In a large skillet, heat butter and oil over medium-high heat; add asparagus stems and tips and cook, stirring occasionally, 3 minutes. Stir in wine and 3/4 teaspoon salt, then add fish; increase heat to high and cook until fish is opaque and cooked through, about 3 minutes. Remove pan from heat.

Cook pasta in the boiling water until al dente; drain and transfer to a large bowl. Add fish mixture including pan juices. Add chopped marjoram and a generous grinding of pepper, then gently toss together. Serve immediately.