Wash and thoroughly dry the mint, parsley, basil, and dill. Removing excess moisture helps keep the dip thick and creamy. Strip the leaves from the stems.
Cut the avocado in half, remove the pit, and scoop the flesh into a blender or food processor.
Add the Greek yogurt, sour cream, fresh herbs, lemon zest, lemon juice, shallot, garlic, salt, and pepper.
Process for about 20–30 seconds, just until combined. The dip should stay slightly textured with visible flecks of herbs; avoid over-blending into a uniform green puree.
Taste and adjust seasoning as needed. Serve immediately, or cover with plastic wrap pressed directly on the surface and refrigerate until ready to use.