Place the mangos, unpeeled, into a large pot of water. They don't need to be submerged. Lightly boil the water until the mangos are soft. A skewer should be able to be inserted into the mangos very easily. Depending on the hardness of your mangos, this can take up to 1 hour.
When completely softened, remove the mangos from the water to cool. When cool enough to handle, remove the peels using a sharp knife. They should come off easily.
Slice the mango fruit away from the center stone in chunks, and purée in a blender. Using either 3 medium mangos or 2 large mangos yields about 2 cups of mango purée. Add the brown sugar, cardamom, black salt and ground pepper to create the aam panna concentrate.
Stir the concentrate into water by the tablespoon. I use 2 - 3 tablespoons for every 8 ounces of water, but it's personal preference.
Taste, and adjust for tartness with lemon juice.
Muddle the mint using a mortar and pestle. I use 4 mint leaves per glass that I'm serving. Add the mint to each glass, ice cubes, and pour the aam panna over it all.