Place quail eggs in a pot and cover with water. Bring to a boil, then reduce heat and simmer for 4 minutes. Remove from heat and let sit for 2 minutes before transferring to an ice bath.

In a mixing bowl, whisk together olive oil, balsamic vinegar, Dijon mustard, minced garlic, salt, and black pepper until well combined.

In a large mixing bowl, combine the mixed salad greens, cherry tomatoes, cucumber, and red onion. Drizzle with the dressing and toss gently to coat.

Halve the hard-boiled quail eggs and arrange them on top of the salad. Serve immediately on a platter.