Preheat a grill or grill pan over medium-high heat. Clean and oil the grates.
Halve the avocado and remove the pit but leave the skin on. Grill cut-side down until grill marks form, 3 to 5 minutes. Flip and grill 2 more minutes. Remove from the heat and let cool slightly. Once cool enough to handle, peel and chop into 1/2-inch cubes. Set aside.
Meanwhile, shred the chicken into large pieces, using mainly the breast meat. Place in a medium bowl and set aside.
Make the dressing: Combine the oil, mustard, honey and lemon juice in a small bowl or jar and whisk together. Season with salt and pepper.
Divide the spring greens mix among 4 bowls or plates. Crumble the feta over the top, sprinkle with the basil, then top with the chicken and grilled avocado. Drizzle with the dressing and serve.