Heat 1 tablespoon oil in a large nonstick skillet over medium-high heat. Add onion to pan; sauté for 5 minutes or until tender and golden brown. Add potatoes, 2 teaspoons sage, and garlic; cook for 25 minutes or until potatoes are tender, stirring occasionally. Stir in beets, 1/4 teaspoon salt, and 1/4 teaspoon pepper; cook 10 minutes, stirring occasionally.
Add water to a large skillet, filling two-thirds full. Bring to a boil; reduce heat, and simmer. Add 1 tablespoon vinegar. Break each egg into a custard cup, and pour gently into pan. Cook for 3 minutes or until desired degree of doneness. Remove eggs from pan using a slotted spoon. Sprinkle 1/2 teaspoon sage evenly over eggs.
Combine remaining 1 tablespoon oil, 2 teaspoons vinegar, 1/4 teaspoon salt, 1/4 teaspoon pepper, 1/2 teaspoon sage, and mustard in a large bowl, stirring with a whisk. Add frisée; toss to coat. Serve with hash and eggs.
Wine match: Merlot. Sweet, earthy beets and the tangy combo of greens and mustard are balanced by The Velvet Devil Merlot (Columbia Valley, Washington State, 2008; $12). The wine's opulent cooked cherry and chocolate aromatic profile give new life to this sadly scorned grape variety. --Alexander Spacher