An extrusion device includes a sculpted extrusion die comprising a pair of mating die lips having sculpted surfaces and defining a die exit for an extrudate. The contour of the sculpted surfaces is substantially similar to the contour of a juxtaposed surface configured for receiving the extrudate from the die exit of the sculpted extrusion die. The sculpted extrusion die preferably comprises a die lip adjustment mechanism for adjusting a thickness of the extrudate exiting the die exit and the thickness of the extrudate received on the juxtaposed surface. The air gap between the die exit of the sculpted extrusion die and the juxtaposed surface preferably is substantially eliminated by adjusting the distance between the sculpted surfaces and the juxtaposed surface. A method of adjusting a thickness of a substantially continuous sheet of extrudate formed using an embodiment of the sculpted extrusion die of the invention is provided.