Split bread horizontally and trim rounded ends of base and any firm portions along sides; save top and trimmings for other uses. Brush base with 1 tbsp. olive oil. Cut lengthwise into thirds, then crosswise into eighths to make 24 squares.
Set bread squares soft side up on a serving board. Arrange a basil leaf on each piece, then add a cucumber slice and mozzarella ball; skewer with toothpicks.
Drizzle with remaining 2 to 3 tbsp. olive oil; season generously with salt and pepper.
MAKE AHEAD: Through step 2, chilled airtight up to 3 hours.