Combine 1 tablespoon olive oil, the oregano, mustard and garlic. Coat the lamb and let stand for 1/2 hour at room temperature.
Heat the remaining 2 tablespoons olive oil in heavy large skillet over high heat. Add the lamb and sear on all sides, turning often to achieve good even color, 1 to 2 minutes per side. Remove from the skillet and chill in the freezer 20 minutes until cold.
Slice the lamb as thinly as possible. Pound the slices between layers of waxed paper until paper-thin. To serve, arrange the lamb slices on a salad plate. Top with Greek Salad and Lamb Turnovers.
In a large mixing bowl, combine the lettuce, tomatoes, cucumbers, feta, olives, olive oil, parsley, scallions and lemon juice, and toss well. Season with salt and pepper.
Preheat the oven to 375 degrees F.
In a large skillet over medium-high heat, add 1 tablespoon butter, garlic and shallots. Cook until soft. Add the ground lamb and cook until done. Remove the mixture to a bowl and cool for 5 minutes. Add the feta, herbs and nutmeg, and season with salt and pepper.
Melt the remaining 1 stick butter in a small saucepan, and then cool. Cover the phyllo stack with 2 overlapping sheets of plastic wrap and then a dampened kitchen towel.
Arrange 1 phyllo sheet on a work surface, with a long side nearest you. Keep the remaining sheets covered. Brush with some melted butter. Top with another phyllo sheet and brush with more butter. Cut the buttered phyllo stack lengthwise into 6 strips.
Put a heaping teaspoon of lamb filling near one corner of a strip on the end nearest you, and then fold the corner of the phyllo over to enclose the filling and form a triangle. Continue folding the strip, like a flag, maintaining a triangle shape. Put the triangle, seam-side down, on a large baking sheet and brush the top with butter. Make more triangles in the same manner, using all of the phyllo sheet and filling, making 12 turnover.
Bake the triangles in the middle of the oven until golden brown, 20 to 25 minutes. Transfer to a rack to cool slightly.