Add all pesto ingredients to a blender and blend until smooth. Season with salt and let the pesto rest.
Cut the zucchini into thick slices. Score them and sprinkle with salt. Let them sit briefly, then pat dry.
Heat some olive oil in a grill pan and sear the zucchini over high heat.
Cook them on the other side until they are nicely colored.
Arrange the grilled zucchini on a plate. Tear the burrata and spread generously over the zucchini. Top with pesto. Garnish with basil leaves and season with pepper, if desired.