Season the chicken breasts with salt and pepper. In a large skillet, heat the olive oil over medium high heat. Add the chicken breasts and sauté until done, about 4 to 5 minute on each side (click here for more detailed directions and a video). Remove the chicken breasts to a plate and set aside; tent them with foil to keep them warm. Do not wipe out the skillet!
Add the leeks to the skillet and sauté over medium high heat for 8 minutes, stirring frequently, until slightly tender. Add the white wine and stir to scrape up all the little flavorful bits that may be stuck to the bottom of the skillet. Simmer for about 2 minutes until the wine reduces by half. Add in the broth, and return to a simmer, stirring occasionally for another 4 minutes until the mixture reduces slightly, by about a third (this is not a precise science. Add the arugula and spinach, stir until they start to wilt, and then add the lemon juice and butter, and stir until the butter is melted and the arugula and spinach are wilted.
You can slice the chicken breasts or leaves them whole. Transfer them to individual plates and spoon the vegetables and sauce over the sauce over the chicken breasts. You can also sliced them all up and serve them with the sauce spooned over on a serving platter.
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Notes
How to Choose Wine for Cooking
You may have heard the kitchen adage that you should only cook with wines that you want to drink. That is 100% true. In the cooking you will burn off most of the actual alcohol, but the flavor will remain to season the dish, and that’s why you should be a fan of the wine in your glass first, then in the dish.