Three crucial aspects still to be overcome to achieve commercial competitiveness of the solar thermochemical production of hydrogen and carbon monoxide are recuperating the heat from the solid phase, achieving continuous or on-demand production beyond the hours of sunshine, and scaling to commercial plant sizes. To tackle all three aspects, we propose a moving brick receiver–reactor (MBR2) design with a solid–solid heat exchanger. The MBR2 consists of porous bricks that are reversibly mounted on a high temperature transport mechanism, a receiver–reactor where the bricks are reduced by passing through the concentrated solar radiation, a solid–solid heat exchanger under partial vacuum in which the reduced bricks transfer heat to the oxidized bricks, a first storage for the reduced bricks, an oxidation reactor, and a second storage for the oxidized bricks. The bricks may be made of any nonvolatile redox material suitable for a thermochemical two-step (TS) water splitting (WS) or carbon dioxide splitting (CDS) cycle. A first thermodynamic analysis shows that the MBR2 may be able to achieve solar-to-chemical conversion efficiencies of approximately 0.25. Additionally, we identify the desired operating conditions and show that the heat exchanger efficiency has to be higher than the fraction of recombination in order to increase the conversion efficiency.