Instructions: For the Homemade Vanilla Ice Cream: Split vanilla beans lengthwise with a sharp paring knife. Gently scrape out all the seeds. Place vanilla-bean scrapings and pods in a medium saucepan with milk. Scald the mixture, cover, and remove from heat. Let steep for 30 minutes.

Combine egg yolks and sugar in the bowl of an electric mixer fitted with the whisk attachment. Beat at medium-high speed until very thick and pale yellow, 3 to 5 minutes. Alternatively, whisk together in a medium bowl. Return milk to stove, and bring just to a simmer. Using a measuring cup or ladle, slowly pour about 1/2 cup of the hot milk mixture into the egg-yolk mixture, whisking constantly on low speed until blended. Keep adding milk mixture, about 1/2 cup at a time, until it has all been added. Whisk until combined.

Pour mixture back into saucepan, and cook over low heat, stirring constantly with a wooden spoon, until mixture is thick enough to coat the back of a spoon, 3 to 5 minutes. The custard should retain a line drawn across the back of the spoon with your finger.

Fill a large bowl with ice and water. Remove pan from heat, and immediately stir in chilled cream to stop the custard from cooking. Pour through a mesh sieve into a medium bowl set in the ice bath, and stir occasionally until cooled. (Discard vanilla-bean pod and strained seeds.) Stir vanilla extract into cooled custard. Cover bowl, and transfer to refrigerator until chilled, at least 30 minutes or overnight.

Pour custard into an ice-cream maker, following the manufacturers instructions. Churn until the ice cream is just set, but not hard. Transfer soft ice cream to an airtight plastic container; freeze at least 4 hours and up to 1 week.

Heat oven to 375 degrees. Scoop out cores of apples with a melon baller. Use the same tool to remove blossom scars at bottoms of apple halves and any skin remaining at stem ends.

Place sugar in a 10-inch ovenproof skillet over medium heat. When sugar begins to melt, stir with a wooden spoon. It will form big lumps at first, but keep cooking and stirring until all the sugar is dissolved and forms a light-amber syrup. As soon as it reaches this stage, remove from heat, and add butter to prevent caramel from overcooking. Stir until butter is melted and incorporated. Arrange apples cut-side up on top of caramel, and tuck rosemary sprigs between them. Place skillet in oven, and bake for 15 minutes. Using tongs, turn apples over; bake until apples are softened, about 15 minutes more.

For the Sour Cream Shortcake Biscuits: Heat oven to 425 degrees. Line a baking sheet with a Silpat or piece of parchment paper.

In a medium bowl, sift together flour, baking powder, baking soda, and salt. Stir in 1/4 cup sugar. Cut in the butter using a pastry blender or two knives until the mixture resembles coarse meal. Stir in sour cream and milk. Scoop the dough into six high mounds evenly spaced on the prepared baking sheet. Sprinkle with remaining 2 tablespoons sugar. Bake until lightly browned, about 15 minutes. Transfer the biscuits to a rack to cool slightly before splitting. (Makes 6 large biscuits)

Using a serrated knife, cut shortcakes in half horizontally. Place the bottom half of each shortcake cut-side up on a large dessert plate. With a small spatula, lift the hot caramelized apple halves from syrup, and place each one cut-side down on a shortcake bottom. Remove and discard rosemary. Return skillet with caramel to stovetop, and bring it to a simmer over medium heat. Gradually whisk in cream. When sauce is smooth, remove from heat.

Top each apple half with a scoop of ice cream. Drizzle the caramel sauce over the top of each dessert, letting it drip onto the plate. Place the shortcake tops over each. Serve immediately.

This recipe yields 6 servings.

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