Toast the coconut in a dry skillet over medium heat, stirring often, until golden brown, 3 to 5 minutes. Transfer to a plate to cool.
In a large bowl, whisk together the heavy cream, milk, sweetened condensed milk, and coconut extract until smooth.
Pour the mixture into a 1½-quart electric ice cream maker and churn until it thickens to a soft-serve consistency, 25 to 30 minutes.
Add the toasted coconut and churn or stir just until evenly combined, about 10 seconds.
Transfer to a freezer-safe container, press plastic wrap against the surface, and freeze until firm and scoopable, 4 to 6 hours.
Notes
Freeze the ice cream maker bowl completely: If your machine uses a freezer bowl, freeze it solid for at least 24 hours. An unfrozen bowl is the top reason ice cream won't thicken, so shake it first and listen for sloshing liquid.Watch the coconut while it toasts: It goes from golden to burnt fast, so stir constantly and pull it off the heat the moment it's evenly golden.Use full-fat dairy: Full-fat cream and whole milk keep it creamy, while low-fat adds water and turns it icy. For dairy-free, use full-fat coconut milk and cream.Store it airtight: Press a piece of plastic wrap against the surface of the ice cream and keep it covered in the coldest part of the freezer. That keeps air off the top so ice crystals and freezer burn don't form.