Reserve 6-8 whole strawberries, cut them in half and set aside. Slice the remaining strawberries and place them in a bowl. Sprinkle with sugar and stir to combine. Let the mixture sit for 15 minutes to macerate the strawberries and bring out their natural sweetness. Afterward, place the mixture in a blender, add 1/2 cup of rose wine, and blend on high until smooth. Strain the mixture through a fine mesh sieve to remove seeds and solids, creating a silky strawberry puree.
Assemble the Sangria. Combine the strawberry puree, the remaining rose wine, and Cointreau in a large pitcher. Stir well to mix. Add the orange and lemon slices, reserved halved strawberries, and fresh mint leaves. Stir gently to distribute the fruit and mint evenly throughout the pitcher.
Chill and Serve. Refrigerate the sangria for at least 30 minutes to let the flavors meld. When ready to serve, pour the sangria into ice-filled glasses. Top each glass with a splash of club soda for a fizzy twist. Garnish with a sprig of fresh mint.