In a medium bowl, whisk together the Dijon mustard, honey, white wine vinegar, salt, and garlic powder until well combined. Slowly drizzle in the vegetable oil while whisking constantly to emulsify the dressing—this creates a creamy, cohesive sauce rather than a separated one. Divide the dressing in half, placing one portion in a shallow dish for marinating the chicken and reserving the other half for finishing the salad. I like to make the dressing first so it has time to meld while I'm preparing the other components.
Place the pounded chicken breasts into the first portion of dressing, coating both sides well, and let marinate for 30 minutes at room temperature—this adds flavor and helps keep the chicken moist during cooking. Heat a large skillet over medium-high heat until hot. Remove the chicken from the marinade (letting excess dressing drip off) and cook for 5-8 minutes per side until golden brown and cooked through, about an internal temperature of 165°F. Transfer to a cutting board and let rest for a few minutes before slicing into strips. I find that letting the chicken rest briefly before cutting keeps it tender rather than stringy.
While the chicken cooks, prepare your salad components: arrange the chopped romaine lettuce as the base in serving bowls or on a large platter. In separate piles, add the halved cherry tomatoes, thinly sliced red onion, diced avocado, crumbled cooked bacon, and quartered hard-boiled eggs. Keep everything organized and visible—the beauty of a Cobb salad is in its presentation with distinct rows or sections of ingredients.
Arrange the warm chicken strips from Step 2 on top of the prepared salad components, nestling them among the other ingredients. Drizzle the reserved honey mustard dressing from Step 1 evenly over the entire salad, making sure to coat all the components. Sprinkle the feta cheese crumbles over the top and season with freshly cracked black pepper to taste. Serve immediately while the chicken is still warm for the best flavor contrast with the fresh vegetables.