Well, it's really awkward. You might want to avoid any direct contact with the neighbor for a while to let the initial shock and embarrassment fade. If the neighbor brings it up, firmly but politely ask them to forget about it and keep it to themselves. It's important to handle this in a way that protects your dignity.
Ignore it as much as you can. Just act like it didn't happen and keep going about your daily life. The more you think about it, the more embarrassed you'll be.
I don't have a specific 'big dick neighbor story' to share. But I can imagine a story where the neighbor with a big heart might be mistaken for being overbearing because of his large stature, which could be misinterpreted as having a 'big dick' attitude, but in reality, he's just a friendly and helpful guy.
A positive 'big dick neighbor story' could be about a neighbor who has a big and generous heart. For example, he might be the kind of person who always shares his home - grown vegetables with everyone in the neighborhood. His 'big' in this sense is about his kindness and abundance of giving, not in a vulgar way.
This is a really tough one. I think you need to consider your friend's reaction too. If your friend seems apologetic and realizes it was a huge mistake, you might be able to move past it more easily. But if your friend doesn't seem to take it seriously, you may need to have a more serious conversation. You could also take some time apart to let the initial shock and embarrassment fade away a bit. In any case, always remember that your privacy is important and you have the right to feel violated by this accidental exposure.
First, stay calm. If it was just a chance sighting and there were no issues, you can simply smile and greet as usual. But if your dog caused some trouble, like scaring them, you should apologize and keep your dog under better control in the future.
You might want to explain what the occasion is for the big cake. For example, if it's for a birthday or anniversary. This can start a nice conversation with your neighbor. And if they seem really interested, you could even share the recipe if you made it yourself.