FIG. 1 is a perspective view of a barbecue basting brush; FIG. 2 is a side elevational view of the design of FIG. 1; FIG. 3 is an opposite side elevational view of the design of FIG. 1; FIG. 4 is a top plan view of the design of FIG. 1; FIG. 5 is a bottom plan view of the design of FIG. 1; FIG. 6 is an end elevational view of the design of FIG. 1; and, FIG. 7 is an opposite end elevational view of the design of FIG. 1.