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We define a dispersionless tau-symmetric bihamiltonian integrable hierarchyon the space of pairs of functions analytic inside/outside the unit circle withsimple poles at $0$/$\infty$ respectively, which extends the dispersionless 2DToda hierarchy of Takasaki and Takebe. Then we construct the deformed flatconnection of the infinite-dimen\-sional Frobenius manifold $M_0$ introduced byCarlet, Dubrovin and Mertens in Math. Ann. 349 (2011) 75--115 and, byexplicitly solving the deformed flatness equations, we prove that the extended2D Toda hierarchy coincides with principal hierarchy of $M_0$.

Principal hierarchies of infinite-dimensional Frobenius manifolds: the extended 2D Toda lattice