Morel and Asparagus Spaghetti

Name: Morel and Asparagus Spaghetti
Ingredients: 5 dried morel mushrooms (about ½ oz.); or substitute 5 fresh morels, halved lengthwise; Kosher salt and freshly ground black pepper; 1 lb. spaghetti; ¼ cup olive oil, plus more for drizzling; 3 Tbsp. unsalted butter; 6 garlic cloves, thinly sliced; 3 medium shallots, finely chopped; 1 lb. asparagus (about 1 bunch), ends trimmed, cut into 1-in. pieces; ¾ cup vegetable stock; ½ cup heavy cream; ¼ cup freshly grated parmesan cheese, plus more for serving; 1 Tbsp. finely grated lemon zest; 2 Tbsp. fresh lemon juice