In a small bowl, whisk together the mustard, vinegar, lemon juice, oregano, garlic powder, salt and pepper until salt is dissolved and mixture smooth. Gradually whisk in olive oil in a thin, steady stream. Continue to whisk the mixture until the oil is thoroughly incorporated and the dressing is thickened. Cover the bowl with plastic wrap until ready to use.
Heat a large skillet over medium-high heat. Add the bacon; cook until crispy, about 3 minutes per side. Remove the bacon from the skillet to a plate; reserve.
To the same skillet, add the sliced mushrooms; sauté until softened, about 5 minutes. Remove the mushrooms from the skillet to a plate; let cool.
In a large serving bowl, toss together the spinach, arugula, onion and cooled mushrooms. Crumble the cooked bacon slices and sprinkle over the top of the salad. Toss with about 1/3 cup of the reserved dressing. Arrange the hard-cooked egg pieces over the top. Serve with remaining dressing on the side. (Extra dressing can be refrigerated, covered, for up to 5 days. Let come to room temperature before using and whisk thoroughly.) Makes 6 servings or 12 appetizer/first course servings.