Slice each zucchini on the diagonal into 12 slices (24 slices total). Brush one side of each zucchini slice with olive oil and season with salt and pepper. Working in 2 batches, place them oil-side down on the grill pan and cook for 2 minutes. Flip each slice and continue grilling until they have grill marks but are still somewhat firm, about 1 minute. Set aside to cool.
Slice the mozzarella into 6 slices, then cut each slice in half. Slice each tomato into 6 slices crosswise (12 slices total).
To make the dressing: Combine the mayonnaise, pesto and vinegar in a small bowl and stir together until well combined.
To assemble the sliders: Top a slice of grilled zucchini with 1 teaspoon of the dressing. Arrange one of the half-slices of mozzarella on the dressed zucchini slice so that it fits the zucchini. Arrange a slice of tomato on top, followed by a basil leaf. Spread a teaspoon of the dressing on a new slice of zucchini and top the stack as if building a sandwich. Secure the slider with a toothpick. Repeat with the remaining ingredients until you have 12 sliders.
Arrange the sliders on a platter, drizzle with balsamic glaze and garnish the platter with more basil.