  Recently, a quantum anomalous Hall state at odd integer filling in moir\'e
stacked MoTe$_2$/WSe$_2$ was convincingly interpreted as a topological Mott
insulator state appearing due to strong interactions in {\it band} basis [P.
Mai, J. Zhao, B. E. Feldman, and P. W. Phillips, Nat. Commun. {\bf 14}, 5999
(2023)]. In this work, we aim to analyze the formation of a topological Mott
insulator due to interactions in {\it orbital} basis instead, being more
natural for systems where interactions originate from the character of $f$ or
$d$ orbitals rather than band flatness. For that reason, we study an
odd-integer filled Anderson lattice model incorporating odd-parity
hybridization between orbitals with different degrees of correlations
introduced in the Hatsugai-Kohmoto spirit. We demonstrate that a topological
Mott insulating state can be realized in a considered model only when weak
intra- and inter-orbital correlations involving dispersive states are taken
into account. Interestingly, we find that all topological transitions between
trivial and topological Mott insulating phases are not accompanied by a
spectral gap closing, consistent with a phenomenon called {\it first-order
topological transition}. Instead, they are signaled by a kink developed in
spectral function at one of the time reversal invariant momenta. We believe
that our approach can provide insightful phenomenology of topological Mott
insulators in spin-orbit coupled $f$ or $d$ electron systems.
