Classic New Orleans Bread Pudding with a Bourbon Sauce

1 teaspoon unsalted butter

4 large eggs

1 cup firmly packed light brown sugar

1/2 teaspoon ground cinnamon

1/8 teaspoon freshly grated nutmeg

1 teaspoon pure vanilla extract

1/4 cup Bourbon

2 cups half-and-half

8 slices day-old French bread, cut into 1/2-inch cubes (about 4 cups)

1/2 cup raisins, or more if desired

Sprigs fresh mint, for garnish

Shaker confectioners’ sugar, for serving

SPICED CREAM

1 1/4 cups heavy cream

1/4 cup granulated sugar

1/2 teaspoon ground cinnamon

1/8 teaspoon freshly grated nutmeg

KENTUCKY BOURBON SAUCE

1 cup heavy cream

1 cup half-and-half

2 teaspoons pure vanilla extract

6 tablespoons sugar

1 tablespoon cornstarch

3 tablespoons bourbon