Prep the chicken: Pat the chicken dry.
Season both sides with 1 teaspoon salt and 1/2 teaspoon black pepper. If the pieces are thick, gently pound them to an even 1/2–3/4 inch for quicker, more even cooking.
Make a quick marinade (optional but great): In a bowl, whisk 1 tablespoon olive oil, 1 tablespoon balsamic vinegar, 1 minced garlic clove, and a pinch of salt and pepper. Coat the chicken and let it sit 10–20 minutes while you prep the salad.
Cook the chicken: Heat a large skillet or grill pan over medium-high.
Add 1 tablespoon olive oil. Cook chicken 4–6 minutes per side, until golden and the internal temperature reaches 165°F (74°C). Transfer to a plate and rest 5 minutes, then slice.
Mix the vinaigrette: In a jar or small bowl, whisk 2 tablespoons olive oil, 2 tablespoons balsamic vinegar, Dijon, remaining minced garlic, honey, 1/4 teaspoon salt, and several grinds of pepper.
Taste and adjust—add a touch more honey if too tart or a splash of vinegar if too mellow.
Prep the salad base: Add mixed greens to a large bowl. Scatter over the tomatoes, mozzarella, and red onion. Add half the basil.
Dress lightly: Drizzle about half the vinaigrette over the salad.
Toss gently with clean hands or tongs until lightly coated. You want the greens glossy, not soggy.
Add the chicken: Layer the sliced chicken over the top. Spoon a bit more vinaigrette over the chicken to season it.
Finish and serve: Top with remaining basil.
Add optional avocado or toasted pine nuts for extra richness and crunch. Taste and adjust salt and pepper. Serve immediately.