Preheat oven to 400 degrees F. Line a baking sheet with parchment paper and set aside.

Combine the cherries, sugar, and cornstarch in a 9-inch square baking dish or alternately use a 9-inch round deep pie pan (see note). Place dish on parchment lined baking sheet (in case of overflow) and roast cherries in preheated oven for 30 minutes, stirring every 15 minutes. Then roast an additional 10-15 minutes, checking every 5 minutes until the juices are thickened and bubbly.

Let cool completely, then chill in the refrigerator.

While cherries are roasting, in a small bowl, whisk 2 tablespoons of the milk with cornstarch until smooth.

In a medium bowl, whisk the goat cheese, cream cheese, and salt until smooth.

Whisk together the remaining milk, cream, sugar, and corn syrup in a 4-quart saucepan and bring to a rolling boil over medium-high heat. Boil for 4 minutes, turning down the heat as needed to maintain a boil and so the mixture doesn't boil over. Remove from heat.

Gradually whisk in the cornstarch slurry and then return to a boil over medium-high heat, whisking continuously until slightly thickened, about 1 minute. Remove from heat.

Gradually pour the hot milk mixture into the bowl with the goat cheese mixture and whisk until smooth.

Pour into a 1-gallon zipper freezer bag and submerge in a large bowl of ice water for about 30 minutes, adding more ice as needed, until cream mixture is cold.

Process ice cream in your ice cream maker following the manufacturer's instructions until thick and creamy.

Pack the ice cream into a quart sized freezable quart-sized container in layers, alternating with roasted cherries and ending with a layer of cherries on top. Do not mix.

Press a sheet of parchment or wax paper directly against the surface of the ice cream and seal with an airtight lid.

Freeze ice cream until firm, at least 4 hours, before serving or up to a week.