Combine pitted cherries with 1/4 cup sugar in a bowl. Toss to coat and let macerate at room temperature for 30 minutes, stirring occasionally, until cherries release their juices.
Heat cream and milk in a medium saucepan over medium heat until steaming and small bubbles form around the edges, about 5 minutes. Do not boil.
Whisk egg yolks with remaining 3/4 cup sugar and salt in a large bowl until thick and pale yellow, about 2 minutes.
Slowly pour 1 cup of the hot cream mixture into the yolk mixture while whisking constantly to temper the eggs. Pour the tempered mixture back into the saucepan.
Cook over medium-low heat, stirring constantly with a wooden spoon, until the custard coats the back of the spoon and reaches 170°F, about 6-8 minutes. Do not let it boil.
Strain custard through a fine-mesh sieve into a clean bowl. Stir in almond extract and vanilla extract. Cover with plastic wrap pressed directly on the surface and refrigerate until completely cold, at least 4 hours or overnight.
Pour chilled custard into your ice cream maker and churn according to manufacturer's instructions until it reaches soft-serve consistency, about 18-22 minutes.
During the last 2 minutes of churning, add the macerated cherries along with their juice. Alternatively, fold cherries in by hand after churning.
Transfer ice cream to an airtight container, press plastic wrap on the surface, and freeze until firm, at least 4 hours before serving.