In a medium bowl, gently mix the ground beef, paprika, Worcestershire sauce, a few dashes of salt and pepper.
Form the beef until about 4 patties...indent the center of each.
In a large Dutch oven, or a skillet, heat 1 tablespoon over medium heat.
Once melted add the mushrooms, and cover with the melted butter.
Add the thyme. Stir.
Add the wine and the stock and simmer until reduced to about 1/4 cup.
Add the salt and black pepper, to taste.
In another skillet, heat the remaining 3 tablespoons of butter.
Add the onions and cook until caramelized...about 15 minutes.
Heat the grill over medium high heat.
Add the burgers and add a couple splashes of Worstershire.
Salt and pepper.
Flip the burgers. Cook for about 6 minutes per side, for medium.
Add the Swiss cheese, until just melted. Removed from the grill.
Butter the split buns, and add to the grill. Cook until lightly browned (about 2 minutes).
Assemble the burgers. Place burgers on the buns, and the add the mushroom sauce and then the caramelized onions on top.