Place potato in a large saucepan; cover with water. Bring to a boil; reduce heat, and simmer 8 minutes or just until tender. Drain well.
Melt 1 teaspoon butter in a large ovenproof nonstick skillet over medium-high heat. Add squash; sauté 5 minutes. Cool slightly.
Whisk together eggs and next 5 ingredients in a large bowl. Add potato and squash.
Melt remaining butter in pan over low heat; add egg mixture (do not stir). Cook, uncovered, 12 minutes or until top is almost set. Sprinkle with cheese.
Wrap handle of pan with foil. Broil 4 minutes or until set. Cut into 8 wedges. Serve immediately.