Lemony Brothy Beans With Asparagus

Name: Lemony Brothy Beans With Asparagus
Ingredients: ⅓ cup plus 1 Tbsp. extra-virgin olive oil; 1 bunch spring onions or scallions, white and pale green and dark green parts separated, thinly sliced; 6 garlic cloves, coarsely chopped; 1 lemon, zest removed in wide strips, lemon halved; 1 cup dried cannellini (white kidney) beans, soaked overnight, drained; 4 cups low-sodium vegetable or chicken broth; ¼ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt, plus more; 1 small bunch asparagus, trimmed, thinly sliced on a diagonal; Country-style bread (for serving)