In a nonstick wok or large nonstick skillet, heat 1 tsp coconut oil on medium-high. Add garlic, greens and ginger and sauté, stirring constantly, until garlic and ginger are fragrant and greens are wilted. Remove from heat and divide among serving bowls. Drizzle with tamari and sesame oil, dividing evenly.
Return wok to medium-high heat and add remaining 1/2 tsp coconut oil. Crack eggs into a small bowl and gently slide eggs into wok. Cook until bottoms are golden brown and whites are just firm and opaque throughout and yolks are runny.
With a spatula, gently slide eggs over top of greens, dividing evenly. If desired, top with Sriracha and pepper, to taste.