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Hull and coarsely chop strawberries. Peel and coarsely chop bananas. Spread the strawberries and bananas on separate sides of one baking sheet or on two sheets. Freeze until solid, at least 12 hours.
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Let the strawberries thaw at room temperature for 15 minutes. Transfer to a food processor; pulse until finely chopped, about 10 pulses. Add the frozen bananas and lemon juice; process until smooth, 1 to 1 1/2 minutes, adding up to 1/4 cup cold water if needed to achieve desired consistency, stopping to scrape down sides of bowl as needed. Serve immediately or, for a firmer texture, transfer to a freezer-safe container and freeze for up to 30 minutes.
Jennifer Causey
Tips
To make ahead: Freeze fruit (Step 1), transfer to separate sealable plastic bags and freeze for up to 6 months.