Wash and dry the cucumbers well, then slice them into 24 even rounds about 1/2-inch thick. If needed, trim a very thin slice from the bottom of any rounded pieces so they sit flat on the serving platter.
Pat the roasted red peppers dry with paper towels so the hummus does not become watery. Drain and rinse the chickpeas thoroughly.
Add the chickpeas, roasted red peppers, olive oil, lemon juice, minced garlic, ground cumin, kosher salt, and black pepper to a food processor. Blend until mostly smooth, stopping to scrape down the sides as needed.
Continue blending until the hummus is creamy and spreadable. If it seems too thick to pipe or spoon neatly, blend in 5 to 10 milliliters of water until the texture loosens slightly.
Taste the hummus and adjust with a little more salt or lemon juice if needed. Transfer it to a bowl or piping bag.
Arrange the cucumber rounds in a single layer on a serving platter. Spoon or pipe an even amount of hummus onto each cucumber slice.
Sprinkle the tops with finely chopped parsley and a light dusting of smoked paprika for color and flavor.
Serve immediately, or chill the topped cucumber bites for up to 30 minutes before serving so they stay cool and fresh.