In a large bowl, combine the flour, sugar, cinnamon, baking soda, nutmeg and salt. In another bowl, beat the eggs, pumpkin and oil until smooth; add to the dry ingredients. Mix until well blended, about 1 minute.
Pour into a greased 13-in. x 9-in. baking pan. Bake at 350° for 40-45 minutes or until a toothpick inserted near the center comes out clean. Cool on a wire rack.
For sauce, combine the brown sugar, flour and salt in a small saucepan. Stir in water and butter; bring to a boil over medium heat. Boil for 3 minutes, stirring constantly. Remove from the heat; stir in vanilla. Cut cake into squares and serve with warm sauce.