Preheat oven to 350°F (180°C) and line a large baking sheet with parchment paper.
Using a sharp knife or mandoline slicer cut zucchini into rounds approximately 2 millimeters thick — slice as evenly as possible for uniform baking — consistent thickness is critical for even results.
Arrange zucchini rounds in a single even layer on prepared parchment-lined baking sheet — do not overlap.
Drizzle or brush a small amount of extra virgin olive oil over each round.
Top each round with a generous even layer of shredded mozzarella covering the entire surface from edge to edge — full coverage is essential as cheese is both the flavor and structural element.
Place baking sheet on center rack of preheated oven and bake for 15 minutes until mozzarella is fully melted bubbling and turning golden at the edges and zucchini underneath has softened and lost significant moisture.
Remove from oven and allow baked rounds to cool on baking sheet for 5–10 minutes until mozzarella sets from molten state into a firmer more cohesive layer bonded to zucchini — do not rush this cooling step.
Take one cooled mozzarella-topped zucchini round and spread a generous layer of softened cream cheese over the cheese surface spreading all the way to the edges.
Layer on a handful of fresh arugula.
Add sliced ripe tomato on top of arugula.
Layer sliced ripe avocado on top of tomato.
Add chosen protein — smoked salmon slices or sliced or shredded grilled chicken — on top of avocado.
Top with a second mozzarella-topped zucchini round placing it mozzarella side facing down toward the filling.
Press gently to hold sandwich together.
Drizzle a small amount of extra virgin olive oil over the top of the assembled sandwich.
Serve immediately.