Heat the oven to 350°F/180°C.
Cut the tortillas into triangles, toss with 1 tablespoon olive oil and the cumin, and arrange on a baking sheet. Bake until crisp and lightly golden, 6 to 8 minutes.
In a large bowl, combine the baby greens, cherry tomatoes, cucumber, red onion, and chickpeas. Drizzle with the remaining 1 tablespoon olive oil and the lemon juice, season with salt, and toss gently to coat.
Arrange the baked falafel over the salad. Scatter the feta cheese and parsley on top, then drizzle with the tahini. Serve with the tortilla chips tucked around the edges for crunch.