In a known method, a SiO2 slip layer is applied to a basic quartz glass body by means of spraying on an SiO2 slip, the slip layer is dried and sintered to form an SiO2-containing functional layer. In order to permit the reproducible production of a functional quartz glass layer, even in the case of surfaces that are curved or inclined with respect to the vertical, having high layer thicknesses which satisfy high requirements on the layer homogeneity, the invention proposes that the slip contain the following components in a dispersion liquid: splintery, amorphous SiO2 granules having a gain size distribution having a D50 value in the range of 3 μm to 30 μm and having a proportion by weight of at least 10% by weight, based on the total solids content; spherical, amorphous SiO2 particles having a particle size distribution having a D50 value in the range of 1 μm to 50 μm and having a proportion by weight of at least 30% by weight, based on the total solids content; SiO2 nano particles having particle sizes of less than 100 nm and having a proportion by weight between 0.2% and 10% by weight, based on the total solids content; and a non-ionic, alkali-free surfactant having a proportion in the range of 0.005 to 0.5%, based on the volume of the dispersion liquid.