Wash the cucamelons. Avoid using bruised or damaged ones.
Add the fresh dill, garlic cloves, and other spices to the bottom of a clean quart jar.
Pack the cucamelons into the jar until full.
Prepare the pickling brine by combining the vinegar, sugar, and salt in a saucepan on the stove. Heat lightly until the sugar and salt dissolve, but then allow the brine to cool to lukewarm/room temperature before adding to the cucamelons.
Pour the brine over the top of the cucamelons until they are completely submerged. If you happen to run out, top off with plain white vinegar if needed. Add optional grape leaves on top now. Place an air-tight lid on the jar.
Refrigerate the jar. During the first 3 to 4 days in the refrigerator, gently tip or shake the jar to wet/rotate the top floating cucamelons - ensuring even pickling and that no "floaters" become dry or moldy. Or, use a glass/ceramic fermenting weight to keep the cucamelons submerged instead.
For optimum flavor, allow the pickled cucamelons to marinate in the refrigerator for at least 1 week before digging in.
Enjoy your pickled cucamelons within 2 to 3 months for best quality and flavor. Maintain refrigerated at all times.