In a large nonstick skillet, melt the butter over medium heat. Add the leeks and a pinch of salt and sauté until tender, about 5 minutes.
Add the asparagus and garlic and sauté until the asparagus is bright green and the garlic is fragrant, 1 minute.
Add the peas and wine. Cook until the wine has almost evaporated, 2 minutes.
Stir in the heavy cream and bring to a simmer. Slowly sprinkle in the Parmesan cheese, whisking continuously, until melted. Season with salt and black pepper. Reduce the heat to low, stirring occasionally.
Cook the pasta according to package directions. Reserve ½ cup of pasta water. Drain the pasta and toss with the olive oil.
If your pasta sauce looks thick, add reserved pasta water, 1 tablespoon at a time, until you reach the desired consistency.
To serve, divide the pappardelle among plates. Spoon the Alfredo sauce over the pasta. Garnish with additional Parmesan cheese and the chopped tarragon.