Step 1

Invert rimmed baking sheet and place sheet of parchment paper or waxed paper on top. Roll dough into 10-inch circle on lightly floured counter. Loosely roll dough around rolling pin and gently unroll it onto prepared sheet. Working around circumference, fold ½ inch of dough under itself and pinch to create 9-inch round with raised rim. Cut three 2-inch slits in center of dough and refrigerate until needed.

Step 2

Adjust oven rack to middle position and heat oven to 400 degrees. Smear butter over bottom of 10-inch ovensafe skillet. Sprinkle ½ cup sugar over butter and shake skillet to distribute sugar in even layer. Sprinkle salt over sugar. Arrange peaches in circular pattern around edge of skillet, nestling fruit snugly. Tuck remaining peaches into center, squeezing in as much fruit as possible (it is not necessary to maintain circular pattern in center).

Step 3

Place skillet over high heat and cook, without stirring fruit, until juice is released and turns from pink to deep amber, 8 to 12 minutes. (If necessary, adjust skillet's placement on burner to even out hot spots and encourage even browning.) Remove skillet from heat. Carefully slide prepared dough over fruit, making sure dough is centered and does not touch edge of skillet. Brush dough lightly with water and sprinkle with remaining 2 tablespoons sugar. Bake until crust is very well browned, 30 to 35 minutes. Transfer skillet to wire rack set in rimmed baking sheet and let cool for 20 minutes.

Step 4

Place inverted plate on top of crust. With 1 hand firmly securing plate, carefully tip skillet over bowl to drain juice (skillet handle may still be hot). When all juice has been transferred to bowl, return skillet to wire rack, remove plate, and shake skillet firmly to redistribute peaches. Carefully invert tart onto plate, then slide tart onto wire rack. (If peaches have shifted during unmolding, gently nudge them back into place with spoon.)

Step 5

Pour juice into now-empty skillet (handle may be hot). Stir in bourbon, if using, and cook over high heat, stirring constantly, until mixture is dark and thick and starting to smoke, 2 to 3 minutes. Return mixture to bowl and let cool until mixture is consistency of honey, 2 to 3 minutes. Brush mixture over peaches. Let tart cool for at least 20 minutes. Cut into wedges and serve.