Pat chicken dry and pound to an even 3/4-inch thickness. Brush with olive oil and season both sides with salt and pepper. Let sit at room temperature while you make the dressing.

Set aside 1/2 cup whole blackberries for garnish. In a small saucepan, combine remaining blackberries, balsamic vinegar, and honey. Bring to a simmer over medium heat and cook 4-5 minutes, mashing berries with a spoon, until syrupy and reduced by half. Strain through a fine mesh sieve into a bowl, pressing to extract all liquid. Discard seeds.

Whisk Dijon mustard into the warm blackberry syrup, then slowly drizzle in olive oil while whisking constantly until emulsified. Season with a pinch of salt. Set aside to cool slightly.

Heat grill pan or outdoor grill to medium-high. Grill chicken 5-6 minutes per side until internal temperature reaches 165°F and juices run clear. Transfer to a cutting board and rest 5 minutes, then slice against the grain into 1/2-inch strips.

In a large bowl, toss greens with about half the dressing. Arrange on a platter or divide among plates. Top with sliced chicken, reserved blackberries, crumbled goat cheese, toasted pecans, and red onion. Drizzle with remaining dressing and serve immediately.