The study of the inclusive production of a pair of charged light hadrons (a “dihadron” system) featuring high transverse momenta and well separated in rapidity represents a clear channel for the test of the BFKL dynamics at the Large Hadron Collider (LHC). This process has much in common with the well-known Mueller–Navelet jet production; however, hadrons can be detected at much smaller values of the transverse momentum than jets, thus allowing to explore an additional kinematic range, supplementary to the one studied with Mueller–Navelet jets. Furthermore, it makes it possible to constrain not only the parton densities (PDFs) for the initial proton, but also the parton fragmentation functions (FFs) describing the detected hadron in the final state. Here, we present the first full NLA BFKL analysis for cross sections and azimuthal angle correlations for dihadrons produced in the LHC kinematic ranges. We make use of the Brodsky–Lapage–Mackenzie optimization method to set the values of the renormalization scale and study the effect of choosing different values for the factorization scale. We also gauge the uncertainty coming from the use of different PDF and FF parametrizations.