We used morel mushrooms, a spring variety known for its nutty flavor and pitted flesh, to flavor these light and fluffy rolls.
Whisk together milk, eggs, and melted butter in a medium bowl; set aside. Whisk together flour and salt in a separate medium bowl. Pour milk mixture into flour mixture; whisk until blended. Cover; let batter stand 1 hour.
Preheat oven to 450 degrees. Put 2 teaspoons oil into each cup of two standard 6-cup popover pans or a large (each cup having a 1-cup capacity) 12-cup muffin tin. Place pans on a rimmed baking sheet. Transfer to oven; heat oil in pans 20 minutes.
Pour batter into popover cups, filling each two-thirds full. Bake (do not open oven while popovers cook) 15 minutes. Reduce oven temperature to 350 degrees; continue to bake popovers until well browned and crusty, about 20 minutes more. Invert popovers to unmold. Transfer to a bowl lined with a clean kitchen towel; cover to keep warm.
Meanwhile, heat remaining 8 tablespoons butter in a large skillet over medium heat. Add shallots; cook, stirring occasionally, until fragrant, about 2 minutes. Add mushrooms; cook, stirring occasionally, until golden, about 5 minutes. Add sherry; cook until liquid is reduced by half, about 2 minutes. Raise heat to medium-high; add cream, and bring to a boil, stirring. Reduce heat to low, and simmer 1 minute. Stir in tarragon, and season with salt and pepper.
To serve, place popovers on plates, and spoon mushroom sauce on top.
If you have leftovers, keep the popovers in an airtight container for up to one day.