Make the compote: Combine the rhubarb, strawberries, orange zest and juice, lemon zest, sugar and vanilla in a bowl. Let macerate at room temperature until juicy, about 30 minutes. Transfer to a saucepan and simmer until syrupy, about 20 minutes; let cool. Blend with an immersion blender until smooth. (The compote will keep in the refrigerator for up to 5 days.)
Make the cocktail: Combine the Aperol, gin, lemon juice and 1/2 ounce of the compote in a cocktail shaker and fill with ice. Shake until very cold, about 1 minute.
Strain the mixture into a wine glass filled with ice. Top with the prosecco and garnish with a strawberry slice.