For the bread pudding: Preheat the oven to 350 degrees F. Grease a baking dish with butter. Add the cubed bread.
In a small saucepan, melt 4 tablespoons butter.
In a large bowl, combine the melted butter, raisins, condensed milk, sugar, and vanilla and whisk together. Add the eggs and whisk again until thoroughly combined.
Pour the custard over the bread and allow to soak for a few minutes. Press the bread into the liquid to help absorb.
Sprinkle the top with the cinnamon and chopped pecans and bake in the oven until the custard is set, about 30 minutes. Stick a paring knife into the center of the pudding. If it comes out with liquid stuck to the knife, cook for a few minutes more until firm. Remove the bread pudding from the oven and allow to cool a bit.
For the peach sauce: In a large saucepan over medium-low heat, melt the butter. Add the peaches, sugar, and liqueur and stir gently until the sugar dissolves. Allow to simmer until the mixture begins to thicken and darken, about 2 minutes. Stir while cooking to avoid burning. Add the heavy cream and stir to combine. Allow to heat through and thicken, about 2 minutes. If the sauce needs additional thickening, combine the cornstarch and water in a small bowl and stir some into the sauce. Remove from the heat and keep warm.
For the rum sauce: Heat a small, nonstick skillet over medium-high heat and add the sugar. Stir and cook until the sugar is melted. Remove from the heat and add the orange liqueur and dark rum. Return to the heat and simmer for 1 minute, and then flambe, if desired, or just let the alcohol burn off.
To plate: Using a ring cutter, cut out rounds of bread pudding and plate in a shallow bowl. Pour the peach sauce over top, and then the rum sauce. Garnish with a dollop of creme fraiche and a small sprig fresh mint.