Dry the bread: spread the brioche cubes on a rimmed baking sheet and leave uncovered for a few hours or overnight, or toast in a 300°F (150°C) oven for 12 to 15 minutes, stirring once, until dry to the touch but not browned.
Preheat the oven to 350°F (175°C). Butter a 9x13-inch baking dish.
Whisk the custard: in a very large bowl, whisk together the pumpkin puree, eggs, heavy cream, milk, brown sugar, cinnamon, ginger, nutmeg, cloves, vanilla, and salt until completely smooth.
Soak the bread: add the brioche cubes and melted butter to the custard and fold gently until every cube is coated. Let the mixture soak for 20 minutes, folding once halfway through, so the bread drinks up the custard.
Assemble: fold in 1/2 cup of the pecans, then transfer the mixture to the prepared baking dish, pressing lightly to even the top. Sprinkle with the remaining 1/4 cup pecans.
Bake covered: cover tightly with buttered foil and bake for 30 minutes.
Bake uncovered: remove the foil and bake 20 to 25 minutes more, until the top is deeply golden and crisp at the edges and the center is set but still slightly jiggly — a knife inserted in the center should come out mostly clean.
Rest and serve: let the pudding rest for 15 minutes so the custard sets for clean scoops. Serve warm, drizzled generously with warm caramel sauce and, if you like, a scoop of vanilla ice cream.