1. In a medium bowl, mix together the mayonnaise, sour cream, Worcestershire sauce, Dijon, paprika, and garlic. Season lightly with salt and pepper. Set aside.
2. In a large bowl, season the beef with 1 teaspoon of salt and 1/4 teaspoon of pepper. Mix to combine but do not overmix.
3. Divide the beef into 4 portions. Shape each into a tight ball, then flatten the ball into a disc. Pinch to make the burger slightly thinner in the center than it is around the edges. Set aside.
4. Heat the oil and 1 tablespoon of the butter in a medium skillet over medium heat. Add the mushrooms and onions. Cook, stirring occasionally, until softened, 5-8 minutes. Season lightly with salt and pepper. Stir. Remove from heat but leave them in the skillet.
5. Heat a large skillet over medium heat. Add the burgers and cook on the first side until deeply seared, 3-4 minutes. Flip and cook on the second side until cooked to an internal temperature of 160F, about 4-6 minutes more.
6. Transfer the burgers to a plate to rest. 
7. Put the skillet of mushrooms back over low heat, just to heat through. 
8. Cut the Kaiser rolls in half. Return the large skillet to the stove and melt the remaining 2 tablespoons of butter over medium heat. Place the rolls in the pan cut-size down, and toast for about 1 minute. Remove the from pan.
9. To assemble the burgers, slather the cut sides of each bun with the mayonnaise mixture. Arrange a piece of lettuce on the bottom buns and top with cooked burger patties. Pile high with mushroom and onions and cover with the top half of the burger bun.

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