White Bean and Roasted Eggplant Hummus

1 (1 1/2-pound) eggplant or 3 Japanese eggplants, trimmed and cut into 2-inch pieces

Olive oil, for drizzling, plus 1/3 cup

Kosher salt, for seasoning, plus 1/2 teaspoon

Freshly ground black pepper, for seasoning, plus 1/4 teaspoon

1 (15-ounce) can cannellini beans, drained and rinsed

1/3 cup loosely packed fresh flat-leaf parsley

3 tablespoons fresh lemon juice (from about 1 lemon)

1 clove garlic

1 hothouse cucumber, cut into 1/4-inch thick slices