Preheat the oven to 450 degrees F and place an oven rack in the middle.
Place the eggplant on a parchment paper-lined baking sheet. Drizzle with olive oil and season with salt and pepper. Roast for 20 to 25 minutes until golden brown. Set aside to cool.
In the bowl of a food processor, combine the cooled eggplant, beans, parsley, lemon juice, garlic, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Pulse until the mixture is coarsely chopped. With the machine running, gradually add 1/3 cup of olive oil until the mixture is creamy. Season with salt and pepper, to taste.
Place the hummus in a dipping bowl and serve with the cucumber slices. Alternatively, spoon the hummus over the cucumber slices and arrange on a serving platter.