In the pitcher, mix together Campari, vermouth, and gin. Add the sliced strawberries and cucumber, let sit for 30 minutes for all the flavors to mingle, then top with ice.
To serve, put a few ice cubes in a rocks glass, pour in 6 ounces (120 to 180 ml) of the Negroni, and float 1 tablespoon of the balsamic vinegar on top.