Toast the pecans in a 12-inch nonstick skillet over medium-high heat, stirring occasionally, until golden brown and fragrant, about 3 minutes.
Off heat, stir in 1 tablespoon butter, maple syrup, and 1/8 teaspoon salt. Return the skillet to medium heat and cook, stirring constantly, until the nuts are dry and glossy, about 45 seconds; transfer to a large plate and set aside.
Wipe out the skillet. Heat the remaining 2 tablespoons butter in the skillet over medium heat; when the foaming subsides, add the shallots, orange zest, and cayenne and cook, stirring occasionally, until the shallots are softened, about 2 minutes.
Stir in the flour until combined, then toss in the green beans.
Add the chicken broth and orange juice; increase the heat to medium-high, cover, and cook until the beans are partly tender but still crisp at the center, about 4 minutes.
Uncover and cook, stirring occasionally, until the beans are tender and the sauce has thickened slightly, about 4 minutes.
Off heat, adjust the seasonings with salt and pepper.
Transfer to a serving dish, sprinkle evenly with the pecans, and serve.