In a small bowl, whisk together Dijon mustard, honey, apple cider vinegar, olive oil, and minced garlic until smooth. Taste and adjust - add more honey if too tart, more mustard if too sweet. Set aside 3 tablespoons for cooking the chicken.

Pat chicken breasts dry and season both sides with 1/2 teaspoon salt and black pepper. If they're thick in the middle, pound to an even 3/4-inch thickness so they cook evenly.

Heat 1 tablespoon olive oil in a large skillet over medium-high heat until shimmering. Add chicken and cook undisturbed for 5-6 minutes until the bottom is deeply golden and releases easily from the pan.

Flip chicken, reduce heat to medium, and spoon the reserved 3 tablespoons dressing over the top. Continue cooking 4-5 minutes until chicken reaches 165°F internally and the glaze is sticky and caramelized in spots. Transfer to a cutting board and rest for 5 minutes.

In a large bowl, combine salad greens, cherry tomatoes, cucumber, and red onion. Drizzle with half the remaining dressing and toss gently to coat. Taste and add the remaining 1/4 teaspoon salt if needed.

Slice chicken against the grain into 1/2-inch strips. Arrange over the dressed greens and drizzle with remaining dressing. Serve immediately while the chicken is still warm.