We demonstrate that the thickness uniformity of chemical vapor deposited graphene monolayers strongly depends on the pre-annealing conditions of the copper foils used as substrates. We show that pre-annealing of copper foils under specific conditions leads to (111)-oriented smooth copper surfaces, while other conditions lead to corrugated surface morphologies. The differences in the morphologies of copper foils pre-annealed under varying conditions can lead to substantially different adlayer number densities. An analysis of the correlation between the adlayer number density and the surface corrugation indicates that the adlayer number density increases with a decrease in the corrugation periodicity and with an increase in the roughness, suggesting that the Ehrlich-Schwoebel barrier on the copper surface promotes formation of the adlayer. The adlayer formation can be suppressed to form centimeter-scale adlayer-free graphene monolayers by obtaining (111)-oriented smooth copper surfaces with minimal corrugation. We explain the strong dependence of surface corrugation on the pre-annealing conditions based on the influence of oxygen adsorption or thermal fluctuation on surface instabilities, such as step bunching, faceting, and step meandering.