Whisk together eggs, milk, salt, garlic powder, and pepper in a large bowl.
Heat olive oil in a large nonstick skillet over medium heat. Add spinach and cook until wilted (about 1 minute). Add beans and reduce heat to medium-low.
Pour in egg mixture and cook low and slow, stirring frequently until eggs are just set (about 5 minutes).
To assemble: Sprinkle each tortilla with cheese, leaving a border. Top with egg mixture, then fold in half.
Heat a clean skillet over medium heat. Cook quesadillas until golden brown and cheese melts, about 2-3 minutes per side.