Peel lemons avoiding the pith as much as possible. Chop lemon peel strips into ¼-inch pieces. Juice lemons to yield ½ cup juice; set aside.

Place lemon peel strips in a small saucepan; add water to cover. Bring to a boil over medium-high; drain lemon peel in a fine wire-mesh strainer, and rinse under cold water. Repeat boiling and rinsing process.

Return lemon peel to saucepan; add sugar and reserved ½ cup lemon juice. Cook over low, stirring occasionally, until sugar dissolves and lemon peel is softened, about 15 minutes. (If mixture starts to brown, stir in 2 tablespoons of water, and continue cooking until peel is softened.) Remove from heat, and set aside. Drain candied lemon peel, reserving syrup for another use. Make the butter beans

Drain 1 can of butter beans. Stir together drained beans, remaining can undrained beans with canning liquid, chicken broth, olive oil, and Calabrian chiles in a medium saucepan. Bring to a simmer over medium. Reduce heat to medium-low; simmer, stirring occasionally, until liquid thickens into a creamy sauce, 10 to 15 minutes. Remove from heat.

Season beans with salt and black pepper; add additional Calabrian chiles to taste. Stir in parsley and lemon juice. Divide beans evenly among serving bowls; garnish each bowl with about 1 teaspoon drained candied lemon peel, reserving remaining candied lemon peel for another use. Drizzle beans with additional olive oil, and serve hot.