Peel and slice the cucumbers into very thin rounds—I like to use a mandoline for uniform thickness, which helps them absorb the brine evenly. Place the sliced cucumbers in a large bowl and toss with the coarse salt. Let them sit undisturbed for 15 minutes; this draws out excess moisture and ensures the cucumbers won't become waterlogged in the final salad. After 15 minutes, squeeze the cucumbers firmly with your hands or press them gently against the side of the bowl to release the accumulated liquid, then discard that liquid and return the cucumbers to the bowl.
In a separate bowl, combine the sugar, white vinegar, and cold water. Stir until the sugar is completely dissolved—this ensures an even, balanced sweetness throughout the salad. I find that dissolving the sugar in a small amount of warm water first (about 2-3 tablespoons) helps it dissolve faster, then you can add the rest of the cold water and vinegar. The brine should taste pleasantly tangy and slightly sweet when tasted on its own.
Pour the vinegar brine mixture over the salted cucumbers from Step 1 and stir gently to combine. Add the finely minced garlic, Hungarian paprika, and freshly ground black pepper, stirring until all seasonings are evenly distributed throughout the salad. The paprika will give the salad its characteristic reddish hue and authentic flavor. Finally, fold in the fresh dill just before serving to preserve its bright, aromatic qualities.