Bring broth and 2 cups water to a simmer in a saucepan over medium-high heat; season with salt. Slowly add polenta, whisking constantly. Simmer, stirring frequently and reducing heat as needed, until thick and creamy, 20 to 25 minutes for regular, or about 5 minutes for quick-cooking. Remove from heat; cover.
Heat a large skillet over medium heat; swirl in oil. Add garlic, celery, and pepper flakes; cook, stirring occasionally, until fragrant, about 2 minutes. Stir in roasted peppers and beans; season with salt and pepper. Cook until heated through, about 1 minute. Add 1/2 cup water and bring to a simmer; cook, mashing some of beans to create a creamy sauce, until thickened slightly, about 2 minutes. Serve over polenta, drizzled with oil and sprinkled with celery leaves.