Adapted from Anne Quatrano's Summerland: Recipes for Celebrating With Southern Hospitality (Rizzoli).
Pudding: Preheat oven to 300 degrees. Butter a 10-inch (14-cup) Bundt pan, preferably nonstick; sprinkle with granulated sugar, tapping out excess.
Whisk together flour, baking powder, and salt in a bowl. Beat 2 sticks butter with granulated sugar and 1 cup brown sugar on medium-high speed until pale and fluffy, about 4 minutes. Add eggs, one at a time, beating until combined and scraping down sides of bowl as necessary. Reduce speed to low; add buttermilk and vanilla and beat until incorporated (mixture will appear curdled). Gradually add flour mixture, then pumpkin, beating just until combined.
Transfer batter to prepared pan; smooth top. Bake until a tester inserted into center comes out with moist crumbs and top begins to crack, 45 to 55 minutes.
Meanwhile, combine syrup, cream, remaining 1 stick butter, and remaining 1 1/2 cups brown sugar in a saucepan. Cook over medium-low heat, stirring frequently, just until butter melts and mixture becomes a smooth, shiny glaze.
Remove pudding from oven and immediately prick all over with a wooden skewer, being sure to penetrate all the way to bottom of pan. Drizzle half of glaze evenly over pudding. Let cool to room temperature in pan on a wire rack, at least 2 1/2 hours.
Hard sauce: Beat butter on medium-high speed until light and fluffy. Reduce speed to low; beat in confectioners' sugar and bourbon.
When ready to serve, preheat oven to 350 degrees. Warm pudding in oven, 15 minutes; remove from oven. Center a heatproof rimmed cake stand or plate over pan, then quickly invert together to release pudding. Rewarm remaining glaze over low heat, stirring until smooth, and pour over pudding, or serve alongside, with hard sauce.