Trim the woody stem ends from the green beans, as needed.
Add 2 tablespoons of olive oil to a 12-inch saute pan and place it over MEDIUM heat. When hot, add the breadcrumbs, garlic, ¼ teaspoon salt, and ¼ teaspoon pepper and cook, stirring constantly, until the bread crumbs are browned and fragrant, about 2 to 3 minutes. Transfer to a plate, sprinkle with the Parmesan, and set aside.
Wipe the empty skillet clean with a paper towel. Add the broth and bring it to a boil over HIGH heat. Add the green beans and return to a boil. Then, reduce the heat to MEDIUM cover and cook for about 2 to 3 minutes until just crisp tender. Be careful not to overcook as the green beans will soften further when sautéed in the next step.
Drain the green beans in a colander and discard the broth.
Wipe the empty skillet dry, return it to MEDIUM heat, and add the remaining 1 tablespoon olive oil. When hot, add the well-drained green beans, and cook, stirring occasionally, for about 2 to 3 minutes or until lightly charred and fork tender. Toss with the remaining ¼ teaspoon salt and ¼ teaspoon pepper and remove the skillet from the heat. Top with the reserved breadcrumb mixture and sprinkle with parsley. Serve immediately.