Tear prosciutto into thin strips, and transfer into a dry nonstick sauté pan set over medium heat.
Cook, stirring, until fat begins to render out and meat begins to brown slightly at the edges, just a few minutes.
Remove 2/3 of prosciutto to a plate and reserve; this will be used later for the melon granita mixture.
Continue to cook the remaining 1/3 of meat until rendered further and edges begin to crisp, about 1 to 2 minutes.
Turn off the heat, transfer meat onto a paper towel-lined plate, and let cool.
Chop into small pieces when cool enough to handle, and refrigerate until needed. Do not wipe any fat from the pan.
Scoop 2 pounds of ripe, sweet melon into a bowl.
Transfer 8 ounces of melon from the bowl into a blender.
Place the bowl with remaining melon into the refrigerator until needed.
Add reserved 2/3 portion of prosciutto into the blender.
Add 1/3 cup of water, and blend until smooth.
Pour melon mixture into the same sauté pan you cooked prosciutto in; add a pinch of salt and 1/4 cup sugar.
Bring to a simmer over medium-high heat, stirring occasionally.
Reduce heat to medium-low, and simmer gently for 15 minutes.
Set a fine mesh strainer over a bowl, pour in melon mixture, and gently press out the liquid.
Cool down to room temperature before proceeding, about 15 minutes. Refrigerate, if desired, for faster cooling.
Liquify remaining 1 1/2 pounds melon in the blender; add to the bowl with prosciutto-infused melon.
Add a drop or two of green food coloring, and stir to combine.
Chef's Note: The final granita will be about half as dark in color as the liquid is before freezing. For a final light melon-green color, use enough food coloring to create at least a medium green liquid.
Pour melon mixture into a casserole dish. Ideally, liquid should be about 1/2-inch deep.
Transfer the casserole into the freezer, uncovered, until the outside edge begins to freeze, 30 to 45 minutes.
Use a fork to mix the partially frozen portion into the liquid portion and stir to combine.
Freeze for about 30 minutes, and repeat.
Continue freezing and scraping with a fork as many times as it takes to create the texture of slightly wet snow.
Cover and freeze until ready to serve.
For candied prosciutto bits, add reserved chopped prosciutto to a dry nonstick sauté pan over medium heat, and sprinkle with 1 teaspoon sugar.
Cook, stirring, until sugar disappears, and prosciutto pieces become shiny.
Transfer onto a plate and let cool. Prosciutto pieces should be crispy when cool.
To serve, use a fork to break up the granita into crystals, as fine or coarse as you like.
Sprinkle with candied prosciutto bits.