Make panna cotta: Pour 2 tbsp. cold water into a medium bowl and stir in gelatin. Let stand until softened, about 5 minutes.
Meanwhile, in a medium saucepan over medium heat, heat cream, 1/3 cup honey, and vanilla bean and seeds, stirring often, until steaming, 4 to 5 minutes. Discard vanilla bean. Whisk cream mixture into gelatin until gelatin fully dissolves. Whisk in yogurt and 1 tbsp. lemon juice until smooth. Set aside.
Prepare melon layer: In a medium bowl, combine 1/2 tsp. lemon zest, 1 tbsp. each honey and lemon juice, and 11/2 tsp. ginger. Drain any liquid from melon, then stir 11/4 cups fruit into lemon mixture.
Set 6 ramekins (6-oz. size) in a rimmed pan. Spoon melon mixture evenly into ramekins. Pour 2/3 cup panna cotta mixture into each ramekin; if needed, stir once or twice so fruit isn’t stuck at the bottom. Chill panna cotta, covered, until set, at least 4 hours. Chill remaining diced melon, lemon juice, and zest separately.
Run a small metal spatula or table knife around each panna cotta to loosen. Let stand at room temperature about 5 minutes, then invert a small plate over each ramekin and give it a firm shake to release panna cotta.
Just before serving, combine remaining honey, ginger, lemon zest and juice, and chopped mint. Drain any juice from reserved melon, then stir melon into lemon mixture. Spoon over panna cotta and top with mint leaves.
MAKE AHEAD: Through step 4, up to 1 day, chilled.