This paper studies the optimal public investment decisions in countries experiencing a resource windfall. To do so, we use an augmented version of the Permanent Income framework with public investment faced with adjustment costs capturing the associated administrative capacity as well as government direct transfers. A key assumption is that those adjustment costs rise with the size of the resource windfall. The main results from the analytical model are threefold. First, a larger resource windfall commands a lower level of public capital but a higher level of redistribution through transfers. Second, weaker administrative capacity lowers the increase in optimal public capital following a resource windfall. Third, higher total factor productivity in the non-resource sector reduces the degree of des-investment in public capital commanded by weaker administrative capacity. We further extend our basic model to allow for "investing in investing" - that is public investment in administrative capacity - by endogenizing the adjustment cost in public investment. Results from the numerical simulations suggest, among other things, that a higher initial stock of public administrative "know how" leads to a higher level of optimal public investment following a resource windfall. Implications for policy are discussed.