Preheat an oven. Pat the chicken dry on all sides, then season with Kosher salt and black pepper.
Heat a large cast-iron skillet over medium-high heat. When very hot, add olive oil. Add chicken thighs, skin side down, then cook until well browned. You’ll know the chicken is ready to flip when it easily releases from the pan. Cook, then use tongs to transfer to a plate.
Add drained, rinsed butter beans, smashed garlic cloves, fresh tarragon (or rosemary).
Add dry white wine, then stir in one bag of fresh baby spinach. Season lightly with a pinch of Kosher salt, then return the browned chicken thighs to the pan, along with any juices. Place on top of the spinach and beans, skin side up.
Place in a preheated oven and cook until the chicken is fully cooked.
Discard tarragon sprigs, then serve immediately with a pinch of flaky sea salt.