Cut the chicken breast into 1/2-inch pieces and measure out all spices into a small bowl—black pepper, chili powder, cumin, and garlic powder. Shred the cheddar cheese from a block (this melts far better than pre-shredded), dice the red pepper into small pieces, and roughly chop the spinach. Having everything prepped ensures you can cook the chicken quickly without interruption.
Heat a skillet over medium-high heat and add the chicken pieces with the spice mixture from Step 1 and the chicken broth. Cook for 3-4 minutes, stirring occasionally, until the chicken is mostly cooked through. Add the diced red pepper and cook for another minute, then stir in the chopped spinach and lime juice. Continue cooking just until the spinach wilts, about 1-2 minutes. I like to taste the filling at this point and adjust the seasoning—sometimes a tiny pinch more salt brings out all those spices beautifully.
Wipe out the skillet and reduce heat to medium. Brush one side of the first tortilla lightly with half of the olive oil and place it oiled-side down in the pan. Let it toast for about 30 seconds until it starts to soften and picks up light color. Quickly sprinkle half of the shredded cheddar directly onto the tortilla in the pan and let it melt for about 30 seconds.
Spoon the chicken and spinach filling from Step 2 onto the cheese-covered tortilla. Brush one side of the second tortilla with the remaining olive oil and place it oiled-side down on top of the filling, pressing gently to adhere. Let the bottom tortilla continue cooking for another 30-45 seconds to develop a light golden crust.
Using a spatula, carefully flip the entire quesadilla and cook the other side for 30-45 seconds until golden and crispy. Transfer to a cutting board, cut into 4 triangular pieces, and arrange on a plate. Serve immediately with salsa and sour cream on the side for dipping. I find that letting the quesadilla rest on the cutting board for just 30 seconds before cutting helps it hold together better.