Combine yogurt, 1 tablespoon of the tarragon, the lemon juice, 1 tablespoon water, 1/4 teaspoon of the salt and 1/8 teaspoon of the pepper in a small bowl. Set aside.
Melt butter in a large skillet over medium-high heat. Add mushrooms and cook 5 to 7 minutes or until slightly softened, stirring occasionally. Stir in remaining 1/2 teaspoon salt, remaining 1/8 teaspoon pepper and remaining 1 tablespoon tarragon. Set aside; cover with a lid or aluminum foil to keep warm.
Meanwhile, bring a large skillet three-quarters full of water to a low simmer. Crack 4 eggs into separate measuring cups; pour into water one by one. Poach eggs for 3 to 4 minutes or until whites are just set. Remove with a slotted spoon and set aside. Repeat with remaining 4 eggs. Reheat first batch of eggs in simmering water if necessary.
Distribute frisée and cooked mushrooms evenly among 4 plates. Top each with 2 poached eggs and drizzle with dressing. Serve each with a slice of pumpernickel.
Replace the 2 poached eggs with a grilled chicken breast.