How to Make It
Preheat oven to 425°F. Place cherries in a single layer in a baking dish. Bake at 425°F until softened, about 15 minutes. Drain; cool completely, about 30 minutes. Place in a small bowl; cover.
Whisk together egg yolks, sugar, and vanilla in a large bowl until light and pale. Combine half-and-half, evaporated milk, corn syrup, and salt in a large saucepan over medium-low. Cook, whisking often, until just simmering, about 10 minutes; remove pan from heat. Gradually pour 1 1/2 cups hot half-and-half mixture in a steady stream into egg mixture, whisking constantly. Add egg mixture to remaining half-and-half mixture in pan.
Return pan to medium-low, and cook, whisking constantly, until mixture is slightly thickened and coats back of a spoon, about 5 minutes. Place in a large bowl; cover. Chill covered bowls of cherries and custard in refrigerator 8 hours or overnight.
Pour chilled custard into freezer bowl of a 2-quart electric ice cream maker, and proceed according to manufacturer’s instructions. Transfer to an airtight freezer-safe container. Drain chilled cherries to remove any juices that might have accumulated overnight; fold cherries and goat cheese into ice cream. Cover and freeze until firm, at least 4 hours.