Cook cherries and honey in a medium saucepan over medium heat, mashing with a potato masher, until jammy and thick, 10 minutes; cool completely. Cherry mixture should measure 1½ cups.

Line a 9x5-inch loaf pan with parchment paper (you can also use two pint freezer containers). 

Combine sweetened condensed milk, vanilla extract, almond extract, and salt in a large bowl. 

Using a stand mixer fitted with the whisk attachment (or a hand held mixer), beat heavy cream on medium high speed until nearly stiff peaks form.

Fold a scoop of whipped cream into sweetened condensed milk until mostly combined. Continue folding whipped cream into sweetened condensed milk in increments until nearly combined; fold in cooled cherry mixture (reserve a spoonful for swirling).

Spread ice cream base into prepared loaf pan or freezer pints. Dollop reserved cherry mixture over top then swirl using a toothpick or skewer. Cover with parchment paper (or lid) and freeze until form, at least 8 hours.