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Bring pot of salted water to boil. Fill a bowl with cold water. Add asparagus to boiling water and blanch 3-4 minutes. Transfer to cold water, drain and cut into 1-inch pieces. Set aside. Keep pot of water hot, but not boiling.
Heat 1 tablespoon olive oil in large skillet over medium heat. Add shallot and cook 2 to 3 minutes, stirring until translucent; then, add mushrooms. Cook 3 minutes, stirring often, until mushrooms begin to soften and sweat. Add garlic and cook until fragrant, 30 seconds to a minute. Season with sea salt and pepper, to taste. Continue to cook mushrooms 2 to 3 minutes until tender and fragrant. Stir in asparagus and remove from heat, but keep warm.
Bring water in pot back to boil and add pasta. Cook al dente. When ready, use a ladle to transfer 1/2 cup of pasta cooking water to pan with vegetables and reserve another 1/2 cup in case you want more to moisten mixture. Drain pasta and toss at once with vegetables. Add more cooking water, if desired. Top with grated parmesan and serve.