Cut the cucumbers into 1/2-inch-thick rounds, and transfer to a colander set in a bowl. Toss well with salt. Refrigerate cucumber rounds 1 hour.
Rinse cucumber rounds well; drain. Pat dry between paper towels. Transfer cucumber slices to a large bowl.
Bring 3 cups water, vinegar, dill seed, and garlic to a boil in a medium saucepan, stirring. Reduce heat; simmer 4 minutes. Let mixture cool slightly, about 10 minutes.
Add chopped dill to cucumber slices, and toss to combine. Pour in the brine. Let cool completely, about 30 minutes. Transfer mixture to airtight containers, and refrigerate at least 1 week (pickles will keep 3 weeks more).