Preparation

• In a medium saucepan, melt the butter over medium-low heat until the milk solids are deep golden brown and the butter has a nutty aroma, about 4 minutes. Whisk in the vinegar and 1 Tbs. of the lemon juice, and set aside. meanwhile, bring a large pot of well-salted water to a boil. cook the pasta according to package directions until al dente. Drain, reserving 1 cup of the pasta cooking water. Return the pasta to the pot and toss with the brown-butter mixture.
• In a large straight-sided skillet, heat the oil over medium-high heat until shimmering. Add the shallots and cook until golden brown in spots, 1 to 2 minutes. Add the mushrooms and cook, stirring frequently, until golden brown and crisp in spots, about 5 minutes. Add the peas and cook, 1 minute, and then add the garlic and cook, about 15 seconds.
• Transfer the pasta to the skillet, and toss with the mushroom mixture. Add the mascarpone, 1/2 cup cooking water, 2 Tbs. of the lemon juice, the tarragon, 2 tsp. of the lemon zest, 1-1/2 tsp. salt, and 1 tsp. pepper, and toss until the cheese melts and the sauce is creamy. Add cooking water as needed.
• Divide the pasta among four plates. Top with the pea shoots. Serve with lemon wedges, and pass the Parmigiano-Reggiano.