Travis Brungardt discusses the strategy of installing exterior continuous insulation in construction. He demonstrates how leaving off the sheathing during build can reduce risks during high winds, as well as make it easier to install R sheathing later. By cantilevering the mudsill and using R6 polyiso bonded to Zip panels, a continuous air and water control barrier can be created. The importance of continuous sealant and air control throughout the build process is emphasized, with attention to details like seal gaskets and taping. Overall, the focus is on reducing risks and ensuring quality in construction practices.