4 large eggs, at room temperature
1 1/2 cups granulated sugar
3 cups store-bought or homemade applesauce, at room temperature
2 sticks unsalted butter, melted and slightly cooled, plus more for the pan
3 cups all-purpose flour
1 tablespoon baking soda
1 teaspoon kosher salt
1/2 teaspoon ground cinnamon
2 cups walnuts, lightly toasted and chopped (optional)