Heterogeneous catalysis, which has served well the petrochemical industry, may valuably contribute towards a bio-based economy by sustainably enabling selective reactions to renewable chemicals. Carbohydrate-containing matter may be obtained from various widespread sources and selectively converted to furanic platform chemicals: furfural (Fur) and 5-(hydroxymethyl)furfural (Hmf). Valuable bioproducts may be obtained from these aldehydes via catalytic transfer hydrogenation (CTH) using alcohols as H-donors under relatively moderate reaction conditions. Hafnium-containing TUD-1 type catalysts were the first of ordered mesoporous silicates explored for the conversion of Fur and Hmf via CTH/alcohol strategies. The materials promoted CTH and acid reactions leading to the furanic ethers. The bioproducts spectrum was broader for the reaction of Fur than of Hmf. A Fur reaction mechanism based on literature data was discussed and supported by kinetic modelling. The influence of the Hf loading and reaction conditions (catalyst load, type of alcohol H-donor, temperature, initial substrate concentration) on the reaction kinetics was studied. The reaction conditions were optimized to maximize the yields of 2-(alkoxymethyl)furan ethers formed from Fur; up to 63% yield was reached at 88% Fur conversion, 4 h/150 °C, using Hf-TUD-1(75), which was a stable catalyst. The Hf-TUD-1(x) catalysts promoted the selective conversion of Hmf to bis(2-alkoxymethyl)furan; e.g., 96% selectivity at 98% Hmf conversion, 3 h/170 °C for Hf-TUD-1(50).