Preheat the oven to 350 degrees F. Bring a large pot of salted water to a boil. Season the pork chops with salt and pepper. Combine the fennel and coriander in a small bowl and rub all over the pork.
Heat 2 tablespoons olive oil in a large skillet over high heat. Add the pork chops and cook until browned, about 1 minute per side. Transfer to a baking sheet and roast in the oven until cooked through, about 5 minutes. Reserve the skillet.
Meanwhile, add the green beans and wax beans to the boiling water and cook until just crisp-tender, about 5 minutes. Reserve 1/4 cup cooking water, then drain.
Add the bacon to the reserved skillet along with 1 tablespoon olive oil; cook over medium heat until crisp, 2 to 3 minutes. Add the shallots and cook, stirring, until tender, about 3 minutes. Add the green and wax beans, butter beans and reserved cooking water. Bring to a simmer and cook until the butter beans are warmed through and the mixture is saucy, 1 to 2 minutes. Add the tarragon and vinegar and season with salt and pepper. Drizzle with the remaining 1 tablespoon olive oil and toss. Serve with the pork chops.