Wash the outside of the watermelon really well. Slice thick slabs of watermelon, then cut into chunks, making sure the rind is intact for some of the cubes and they have a nice amount of fruit still attached. (You should have about 12 cups.)
Transfer the chunks to a large punch bowl or drink dispenser. Add in the rosé.
Cover and chill in the fridge for at least 6 hours (ideally 12-24. The longer the better.)
Right before serving, stir in the chilled Proseco or Moscato.
Serve in glasses, using tongs to add individual pieces of watermelon along with a slice of lime.
NOTE: Prosecco is very fruity and less sweet, whereas Moscato is very sweet, fragrant, and less acidic. Choose whichever one you prefer.