To make the dipping sauce:
Melt the butter in a medium frying pan over moderate heat, and add the sliced onions. Cook, stirring occasionally, until the onions soften, then caramelize. This should take between 10 and 15 minutes. The lower the heat, the longer it takes, but the less likely you are to burn the onions.

Once the onions are a medium brown, remove from the heat and add the vinegar.

Place the onions and vinegar into a small food processor. Add the honey and mustard, and process or blend until smooth.

Add the mayonnaise and salt and pepper to taste, stirring to combine. Refrigerate, covered, until ready to serve.

To make the zucchini sticks:
Place the zucchini sticks in a colander over a bowl and sprinkle with the tablespoon of salt. Let the zucchini drain for 1 hour or longer; rinse and pat dry.
Preheat the oven to 425°F. Line a baking sheet with parchment, and spray the parchment with olive oil.

Set up your zucchini dredging by placing the flour in a shallow bowl, the eggs in another shallow bowl, and the panko, parmesan, and oregano in a third shallow bowl. Dredge sticks in the flour, then egg, then roll in the crumb mixture. Place the sticks on the prepared baking sheet.

Bake sticks for 12 minutes, turn over, and bake for an additional 8 minutes, until golden brown and crisp.

Serve immediately, with caramelized onion dip.