Combine flour, cornmeal, sugar, soda, and salt in a large mixing bowl; mix well. Cut in softened butter with a pastry blender until mixture resembles coarse meal. Combine water and vinegar; add to flour mixture, stirring until dry ingredients are moistened.
Turn dough out onto a floured surface; knead 4 to 5 times. (Dough will be soft. )
Shape dough into 1/2-inch balls. Using a floured rolling pin, roll each ball into a 2-inch circle. Transfer circles to ungreased baking sheets. Brush each with melted butter; sprinkle with sesame seeds. Using a spatula, press sesame seeds firmly into crackers. Bake at 375° for 10 minutes or until lightly browned. Remove crackers from baking sheets, and cool on wire racks. Serve with soups or stews.