Spiralize zucchini into noodles using a spiralizer with the medium blade. Place noodles in a colander, sprinkle with 1/4 teaspoon salt, and let drain for 10 minutes.

While zucchini drains, pat chicken breast dry and season both sides with salt and pepper. Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Cook chicken 4-5 minutes per side until golden and internal temperature reaches 165°F. Transfer to a cutting board and let rest 3 minutes, then slice against the grain.

In a small bowl, whisk together remaining 1 tablespoon olive oil, lemon juice, Dijon mustard, minced garlic, and a pinch of salt and pepper until emulsified.

Gently squeeze the drained zoodles to remove excess moisture (do not rinse). Pat dry with paper towels.

In a large bowl, combine zoodles, halved cherry tomatoes, sliced red onion, and half the vinaigrette. Toss gently to coat.

Divide zoodle mixture between two bowls. Top with sliced chicken and remaining vinaigrette. Sprinkle with fresh basil and feta cheese if using. Serve immediately.