Artificial lipid membranes incorporating proteins have frequently been used as models for the dynamic organization of biological structures in living cells as well as in the development of biology-inspired technologies. We report here on the experimental demonstration and characterization of a pattern-forming process that occurs in a lipid bilayer membrane adhered via biotin-avidin binding to a second lipid membrane that is supported by a solid substrate. Adhesion regions are roughly circular with a diameter of about 25 mu m. Using confocal fluorescence microscopy, we record time series of dynamic fingering patterns that grow in the upper lipid membrane and intermembrane biotin-avidin bonds. The fingers are micrometer-scale elongated pores that grow from the edge of an already-stabilized hole. Finger growth is saltatory on the scale of tens of seconds. We find that as the fingers grow and the density of adhesion proteins increases, the rate of finger growth decreases exponentially and the width of newly formed fingers decreases linearly. We show that these findings are consistent with a thermodynamic description of dynamic pore formation and stabilization.