Combine all feta dip ingredients in a blender or food processor and blend until smooth, adding more olive oil if needed. Transfer to a container and refrigerate for up to 1 week.
Halve the zucchini lengthwise and score the cut sides diagonally with 5 to 6 shallow cuts, taking care not to cut through. Season generously with salt and pepper.
Heat a skillet over medium heat and add about 3 tablespoons of olive oil. Sear the zucchini cut side down until browned, 3 to 4 minutes. Flip and cook until tender, another 3 to 4 minutes.
Transfer to a paper towel–lined plate and let rest 5 minutes before serving.
Spread the feta dip on a serving plate, layer with zucchini slices, and finish with salt, hot sauce, pistachios, and basil.