1. In a large bowl, whisk together yogurt, cream, sugar, and vanilla until sugar dissolves, about 2 minutes. In a small bowl, whisk together 1 cup vanilla mixture and cocoa powder until smooth; transfer to a quart-size zip-top bag. In a food processor, combine 1/2 cup vanilla mixture and strawberries. Puree until smooth, 1 to 2 minutes; transfer to a liquid measuring cup. Transfer remaining vanilla mixture to another quart-size zip-top bag.

2. With scissors, snip a 1/2-inch hole in one corner of bag with cocoa mixture and pipe into eight 3-ounce ice-pop molds, dividing evenly. Gently tap molds on a work surface to smooth (wiping away any smudges on sides with a paper towel if desired). With scissors, snip a 1/2-inch hole in one corner of bag with vanilla mixture and pipe an even layer over chocolate mixture, dividing evenly. Gently tap molds on work surface to smooth (wiping sides if desired). Top with strawberry mixture. Insert ice-pop sticks and freeze until solid, about 6 hours (or up to 2 weeks).