Place potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 20 minutes. Drain and cool. Chop potatoes and transfer into a large salad bowl.

Place the bacon in a large skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain the bacon slices on paper towels. Crumble bacon when cool.

Stir mayonnaise, crumbled bacon, cucumber, red onion, 3 chopped eggs, celery, 1/2 cup parsley, and 1 tablespoon paprika into the potatoes until thoroughly combined. Season to taste with salt and black pepper. Garnish salad with slices of hard-cooked egg, 3 sprigs of fresh parsley, and a pinch of paprika.