Chicken and Dropped Dumplings Recipe | Alton Brown

Ingredients

• 1 (5- to 5 1/2-pound) chicken, giblets removed
• 3 1/2 teaspoons kosher salt, divided, plus more to taste
• 7 to 9 cups water ((to just under the max fill line))
• 3 tablespoons unsalted butter
• 1/2 cup plus 1 tablespoon all-purpose flour
• 2 large eggs, at room temperature
• Freshly ground black pepper, to taste