This dessert is one of our sexy vanilla recipes.
Add butter to the bowl of a stand mixer with a paddle attachment. Beat on medium-high until fluffy, about 2 minutes. Slowly add 1 cup sugar until blended, scraping down the sides. Increase to high, and beat for 2 minutes. Reduce to low, and add eggs one at a time, then beat in 2 tablespoons vanilla extract.
With mixer on low, alternately add coffee-flour mixture and sour cream to bowl in several parts (ending with dry mixture) until smooth and blended.
Spoon into prepared pan, and bake until a toothpick inserted in the center comes out clean, 35 to 45 minutes. Cool on a rack for 10 minutes, then run a knife around edges to loosen cake and invert onto a plate. Cool completely.
Make crème anglaise by whisking 1/4 cup sugar and egg yolks in a medium bowl until combined. Prepare an ice bath by placing a medium bowl in a shallow bowl of ice water; set aside. Split vanilla bean and scrape out seeds; add seeds and pod to a saucepan with half-and-half. Cook on low until small bubbles form around rim, 3 to 5 minutes.
Whisk half of hot half-and-half into sugar-egg mixture in a thin stream, then pour mixture into saucepan. Cook over medium heat, stirring constantly with a wooden spoon, until sauce has thickened slightly, 3 to 5 minutes. Immediately strain sauce into bowl of prepared ice bath to stop the cooking (discard pod). Add 1 teaspoon extract; stir to combine. Serve right away or refrigerate until chilled.
Cut cake into thick slices or cubes. Pour crème anglaise on top, or pass it around in a bowl as a dipping sauce.