Hull strawberries and place in a 3- to 4-quart pan. Coarsely mash with a potato masher. Add 1/2 cup sugar and stir occasionally over medium-high heat until mixture begins to bubble, 2 to 3 minutes.
Nest pan in a bowl of ice water and stir often until cold, 5 to 10 minutes. Remove pan from ice water.
Add remaining 1/2 cup sugar, sour cream, half-and-half, vanilla, and almond extract to berries; stir until blended (mixture will be streaked).
Pour into an ice cream maker (1 1/2-qt. or larger capacity). Freeze according to manufacturer's directions until mixture is softly frozen, dasher is hard to turn, or machine stops.
Spoon out and serve softly frozen or, to scoop, freeze airtight about 3 hours; store airtight in the freezer up to 1 week.
Nutritional analysis per 1/2 cup.