Cook the potatoes. Place potatoes in a large pot of boiling water; cook until tender, about 15 - 20 minutes. Remove from heat, drain and let cool slightly.
Make the dressing. While potatoes are cooking, combine mayonnaise, vinegar and mustard in a small bowl. Whisk until blended. Add tarragon, oregano, salt and pepper, mix well.
Prepare the salad. Place potatoes in a large bowl and add minced onion, stir to combine. Add dressing to potato mixture and stir to combine. Chill for at least one hour before serving.
Make the burger patties. Add all of the burger ingredients to a mixing bowl and mix to combine. Divide the mixture into 4 equal parts and form into patties.
Grill the burgers. Heat a gas grill to medium heat. Place the patties on the grill and cook for 5 minutes. Flip the burgers and cook for an additional 5 minutes (until the internal temperature reaches 165°F) Turn the heat to low and add a slice of swiss cheese to each burger. Close the grill cover and cook for 2 minutes or until cheese melts.
Assemble and serve. Remove the burgers from the grill. Spread the bottom half of each bun with mayo, top with burger and avocado slices. Serve immediately with a side of potato salad.