1. To make the Burger buns (10 buns): Mix the egg, water, oil, sugar and yeast together until the yeast dissolves.
2. Combine the two types of flour with the salt. Add ⅔ of the flour mix to the liquid mixture and stir to combine.
3. Continue adding the remaining flour mixture until you can touch the dough without it sticking to your fingers. Knead the dough for about 5 minutes, then a small cube of cold butter. Knead until it is incorporated into the dough.
4. Let the dough rise under a cloth for one hour. Place the dough on a lightly floured board. Divide the dough into 10 equal portions.
5. Roll them into buns and place them on a baking sheet. Let them rise for another 30 min. Brush with egg and sprinkle with sesame seeds.
6. Bake the buns at 400°F for about 12-15 minutes. They should have a bit of color and sound hollow when you knock on their bottoms.
7. For the Red onion relish: Cut the onions into thin strips and fry them over low to medium heat in butter until lightly caramelized. It will take approximately 10-15 minutes.
8. Add thyme, brown sugar, red wine and vinegar. Cook until the liquid has boiled down. Season with salt and pepper.
9. Honey mustard dressing
10. Combine the mayonnaise, honey and mustard. Season with lemon juice, salt and pepper to taste.
11. Additional ingredients (for 6 burgers).
12. Form the mean into 6 patties of equal size. Season with salt and pepper. Cook on a scorching-hot grill for 3-4 minutes on each side – time will vary slightly depending on how hot the grill is. If your grill doesn’t get as hot, you may need to leave them on a few extra minutes.
13. After flipping the burgers, add the cheese on the grilled side. When you’re done grilling the meat, you can use the grill to warm up the burger buns.
14. Split the buns and spread dressing on both halves. Add a leaf of lettuce and a slice of tomato. Top with the meat and relish. Close the burger. Enjoy!