Rinse the berries under cold water and remove their leaves. Cut the berries into quarters or thirds, put them in a bowl, and sprinkle them with sugar. Set aside for an hour or so. When an hour has passed, lightly whip the cream—you want it thick enough to lie in folds, but not so stiff that it stands in peaks. (This won’t take long if you are using an electric hand mixer.)
Put the sugar-sprinkled strawberries, along with any juice that’s seeped to the bottom of the bowl, into a food processor and whiz until smooth. Next, stir the processed sugar-strawberries into the cream. How thoroughly you blend the two is up to you. Next, transfer the mixture to a freezer-safe container such as a deep baking dish, or bowl made of plastic or stainless steel. Level the top, and cover with a lid or a piece of plastic wrap. You’ll need to stick close to home while the mixture freezes from solid to liquid, stirring it occasionally to break up the ice crystals.
Once you’ve put it in the freezer, check the mixture after 45 minutes; once it freezes near the edges, stir it vigorously with a spatula or whisk. Return it to the freezer and continue this task every 30 minutes or so, until the ice cream is frozen. It will take 3 to 4 hours, maybe more depending on your freezer, to be ready.
Remove the ice cream from the freezer about fifteen to twenty minutes before serving.