Process the bread in a food processor to produce even, fine crumbs, about ten 1 second pulses. Heat 1 tablspoon of the butter in a large skillet over medium-high heat; when melted, add the bread crumbs and cook, stirring frequently until golden brown, 3 to 5 minutes. Transfer to a medium bowl and stir in 1/4 teaspoon salt, 1/8 teaspoon ground black pepper and the Parmesan cheese, set aside.

​Wipe out your skillet. Add the remaining 2 tablespoons of butter, the garlic and 1/4 teaspoon salt; cook over medium heat, stirring constantly, until the garlic is golden, 3 to 5 minutes. Stir in the flour, red pepper flakes and thyme, then toss in the green beans. Add the chicken broth and 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. Turn off heat, stir in the lemon juice and adjust the seasonings with salt and black pepper to taste.

​Transfer to a serving dish, sprinkle evenly with the bread crumbs and serve.