Pumpkin Spice Latte Sweet Rolls

Stir together warm coffee, granulated sugar, and yeast in a medium bowl; let stand until foamy, about 5 minutes. Stir together flour, 2½ teaspoons pie spice, and salt by hand in the bowl of a stand mixer. Add yeast mixture, pumpkin, melted butter, and egg; using the paddle attachment, beat at low speed until just combined. Switch to the dough hook attachment; beat at medium speed until dough is smooth and elastic, about 15 minutes. (Dough will be slightly sticky but manageable with lightly floured hands). Spray a large bowl with cooking spray. Place dough in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (75°) until doubled in size, about 1 hour. Place 1 package cream cheese, 1 cup confectioners’ sugar, instant espresso, and remaining 2 tablespoons pie spice in a medium bowl; beat with a mixer at medium speed until combined. Spray a 12-inch cast-iron skillet with cooking spray. Punch down dough. On a lightly floured surface, roll dough into a 20x15-inch rectangle. Spread cream cheese mixture in an even layer onto dough, leaving a ½-inch border along one long side. Starting with long side opposite border, roll dough into a log; pinch seam to seal. Using a serrated knife, trim ends, and cut log into 10 (2-inch) slices. Place slices in prepared skillet. Cover and let rise until puffed, 35 to 45 minutes. Preheat oven to 350°. Bake, uncovered, until golden brown, 35 to 40 minutes. Whisk together milk, vanilla, remaining 1 package cream cheese, and remaining 2 cups confectioners’ sugar until combined. Spread onto warm rolls.

Garnish with pie spice, if desired. Serve warm.