Cylindrical optical components of quartz glass are known, which have an inner zone made of an inner zone glass, which extends in the direction of the longitudinal axis and is surrounded by a jacket zone made of a jacket zone glass, the average wall thickness thereof varying at least over a part of its length in the direction of the longitudinal axis of the component. The aim of the invention is to provide a method that allows a simple and cost-effective production of such an optical component from quartz glass. A method is proposed according to the invention, comprising the following method steps: (a) providing a first parison made of an inner zone glass, which has a first contact surface on the end face, said contact surface having a conical external contour; (b) providing a second parison from the jacket zone glass; (c) embedding the contact surface with a conical external contour into the jacket zone glass and welding the contact surface to the jacket zone glass, thereby forming a composite parison which has a cone-shaped inner zone area of inner zone glass in a contact area, said inner zone area being surrounded by a jacket zone area having the shape of an inner cone; and (d) elongation of the composite parison to form the optical component or a preproduct of the component.