Mix 3 cups flour and brown sugar in a large bowl; cut in softened butter with a knife or pastry blender until mixture resembles coarse crumbs. Reserve 1 1/2 cups flour mixture; pat remainder into the bottom of a 9x13-inch pan.
Bake in preheated oven until crust is lightly browned, about 15 minutes.
Beat eggs in a large bowl; mix 1/4 cup flour, white sugar, half-and-half, and salt into eggs, beating until smooth.
Sprinkle chopped rhubarb over baked crust. Pour egg mixture over rhubarb; top with reserved flour mixture.
Bake in preheated oven until eggs are set and lightly browned, 40 to 45 minutes.