Slice the zucchinis crosswise into rounds (at least 12 slices from each zucchini- you may have extra).
Toss the zucchini slices in a bowl with 1-2 tablespoons of olive oil. Season with salt and pepper and toss again.
Grill the zucchini slices on each side just until you have char marks and the slices are tender but not mushy. You can use a barbecue grill, a grate over a campfire, a grill pan on the stovetop, or arrange the slices in a single layer on a cookie sheet and broil them in the oven, turning them to lightly brown both sides.
Cut each of the mozzarella slices into quarters. Halve the anchovy slices, and tear each basil leaf in half.
Make 12 stacks by layering the zucchini slices, cheese pieces, basil leaves, and anchovies. Each stack should contain 4 zucchini slices, 3 pieces of cheese, 1 anchovy, and 1 basil leaf. Drizzle a few drops of balsamic glaze between a couple of the layers in each stack.
Thread an olive (or cherry tomato) onto each skewer and poke them down through the stack, with the olive on top, to keep the layers together. Arrange the zucchini stacks on a platter and drizzle them with a bit more balsamic glaze. Serve at room temperature.
Makes 12 zucchini stacks, serving 4 to 6 as appetizers or veggies side dishes.