For the honey ice cream: Put the cream, half-and-half and honey in a medium saucepot and bring to a boil. Whisk the eggs and salt together in a large bowl. Slowly whisk the hot cream into the eggs, 1 cup at a time. Once all of the cream has been added, pour the mixture back into the pot and return it to the stove. Cook over medium-low heat while stirring constantly with a wooden spoon. The mixture will thicken to where it coats the back of the spoon.
Strain through a fine sieve into a clean bowl and chill until cold. Spin the ice cream in an ice cream maker according to the machine's directions, and freeze until it hardens.
For the carousel cookies: Add the flour, oats, apricots, plums, sugar, baking powder and salt to the bowl of a food processor and process until a coarse meal is formed. Add the cheese and butter and pulse just to combine. Whisk the milk and egg yolk together and stream into the food processor while the machine is running. Process until the dough begins to form a ball. Roll the dough into a log on a lightly floured surface, wrap tightly in parchment paper or plastic wrap and refrigerate for 1 to 2 hours.
Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper.
Unwrap the dough and cut into 1/8- to 1/4-inch-thick slices. Place the slices on the baking sheets, allowing 1/2 inch between each cookie, sprinkle lightly with turbinado sugar and bake for 10 to 12 minutes. Allow to cool completely.
To make the ice cream sandwiches: Sandwich some honey ice cream (or your favorite vanilla ice cream) between 2 carousel cookies; repeat with the remaining ice cream and cookies. Wrap the ice cream sandwiches in parchment paper and freeze until you are ready to eat.
NotesThis recipe was provided by a chef, restaurant or culinary professional and may have been scaled down from a bulk recipe. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.