In this talk, I will present a singular perturbation problem for second-order Hamilton–Jacobi equations, focusing on the asymptotic behavior of solutions as the perturbation parameter vanishes. The analysis is carried out in the framework of viscosity solutions for equations in the Wasserstein space, using the perturbed test function method adapted to this infinite-dimensional setting. I will also discuss connections with the homogenization of systems of slow–fast McKean–Vlasov stochastic differential equations.