Pat 4 cod fillets dry with paper towels and season with ½ teaspoon table salt.
Melt 4 tablespoons unsalted butter in 12-inch nonstick skillet over medium heat.
Add 1 leek and remaining ¼ teaspoon salt and cook, stirring occasionally, until lightly browned, 4 to 6 minutes.
Stir in 3 thinly sliced garlic cloves and ¼ teaspoon red pepper flakes and cook until fragrant, about 30 seconds.
Stir in 1 can butter beans and their liquid.
Nestle fish into skillet and bring to simmer.
Cover; reduce heat to low; and cook until fish flakes apart when gently prodded with paring knife and registers 140 degrees, 8 to 12 minutes.
Carefully transfer fish to plate.
Increase heat to medium-high and stir in 5 cups baby spinach.
Cook, stirring occasionally, until spinach is wilted, about 2 minutes.
Stir in 1 tablespoon lemon juice and 1 tablespoon chopped dill and season with salt to taste.
Return cod to skillet and sprinkle with remaining 1 tablespoon chopped dill. Serve.
