On a lightly floured surface, unroll piecrust dough. Using a 3 1⁄4-inch fluted square cutter dipped in flour, cut 12 squares from dough. Press dough squares into bottoms and up sides of 12 (3 1⁄4-inch) square tartlet pans with removable bottoms, pinching corners of dough slightly to elongate. Freeze for 15 minutes.
Line each tartlet shell with parchment paper and fill with pie weights or dried beans.
Bake for 7 minutes. Remove pie weights and parchment. Bake until very lightly browned, 2 to 3 minutes more. Let cool completely in pans on wire racks.
In a medium sauté pan, heat oil over medium heat. Add butternut squash; cook, stirring occasionally, until tender, approximately 5 minutes. Remove from pan.
Add mushrooms to the same pan; cook, stirring occasionally, until tender, approximately 5 minutes. Remove from pan.
Add butter to the pan; cook, stirring frequently, until golden brown, 1 to 2 minutes. Add sage to butter. Return squash and mushrooms to pan and season with sea salt.
Reduce oven temperature to 400°.
Divide cheese evenly among prepared tartlet shells. Top evenly with squash and mushroom mixture.
Bake until cheese is melted and bubbly, 5 to 10 minutes. Let cool slightly before removing from pans.
Garnish with sage, if desired. Serve warm or at room temperature.
Recipe by TeaTime Magazine at https://teatimemagazine.com/butternut-squash-mushroom-tartlets/