Preheat oven to 400° Place sweetpotato on a foil-lined baking sheet. Bake until soft, about 45 minutes; puree in food processor.
Coat 12 muffin cups with cooking spray. Divide bread pieces evenly among all 12 muffin cups.
In a medium bowl, beat 3 whole eggs. Add milk, 1/2 cup half-and-half, 1 teaspoon vanilla and the brown sugar; whisk until well-combined. Whisk in pureed sweetpotato.
Pour egg mixture into muffin cups over bread, dividing evenly. Cover muffin tins with plastic wrap; refrigerate overnight.
To make the Crème Anglaise, in a large saucepan over medium heat, heat the remaining 2 cups half-and-half until just simmering, about 5 minutes.
In a medium bowl, whisk together the granulated sugar and 4 egg yolks. Slowly add half of half-and-half mixture to the egg yolk mixture, whisking constantly.
Pour half-and-half and egg mixture back into saucepan; raise heat to medium. Cook, stirring constantly with a wooden spoon until sauce has thickened and coats back of spoon, about 5 minutes. Remove from heat immediately; stir in vanilla extract and cardamom. Pour through strainer into a heat-proof bowl. Cover and refrigerate overnight.
Next day, preheat oven to 325°F degrees. Remove plastic wrap from muffin tins. With a spoon, push bread down into the egg mixture. Bake until edges are golden but not brown, about 35 minutes.
Remove from oven. Loosen cups by running a butter knife along the edges before popping them out. Serve with chilled Crème Anglaise.