Cut cucumbers crosswise into 1/8-inch-thick slices; then toss with kosher salt in a bowl and let stand 15 minutes. Rinse and drain cucumbers and pat dry with paper towels.
Whisk together vinegar, sugar, mustard, horseradish, and dill until sugar is dissolved. Stir in cucumber and let stand at least 5 minutes.
Slice bread and serve with pickles and cheese.
Note: Pickles can be made 2 to 4 hours ahead and chilled, covered.