Heat a large nonstick skillet over medium-high heat.
Add 1 tablespoon oil; swirl to coat.
Add potato slices, onion, and salt; saut 6 minutes, stirring after 3 minutes. Saut 6 additional minutes or until potato is tender, stirring occasionally, adding garlic during last 1 minute of cooking time.
Remove from heat; stir in thyme and next 3 ingredients (through pepper).
Remove potato mixture from pan; keep warm.
Heat pan over medium-low heat.
Add remaining 1 tablespoon oil; swirl to coat.
Add eggs to pan; cook 1 minute or until whites are just set around edges. Carefully turn eggs over; cook 1 minute or until whites are set.