Preheat oven at 400 degrees F.
Place a 10 inch deep oven proof dish or cast iron pan in the middle on the lower rack to heat up.
With an electric mixer beat eggs until a light foamy yellow.
Add milk flour, garlic powder, dill, paprika, red pepper and lemon zest beat until a thin smooth batter.
With a paper towel pat dry the crab meat add to batter mix well.
Without removing the oven proof dish out of the oven, pull oven rack out and add the 4 tablespoons of butter to the hot dish. Swirl around until the butter is melted; pour batter on top of the butter and push back in the oven rack to center the dish.
Bake 25 minutes.
On the stove top in a non-stick frying pan on medium high heat sauté mushrooms in oil until golden brown. Set aside.
In a small sauce pan on stove top, melt ¼ cup butter and add the sauce mix package.Whisk for a minute.
Add 1 cup of milk whisk on medium high until sauce thickens.
Remove Dutch baby from oven and drizzle with fresh lemon juice.
Serve immediately. Top with Béarnaise mushroom sauce and sprinkle with chives.