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We construct a continuous 1-parameter family of smooth complete Ricci-flatmetrics of cohomogeneity one on vector bundles over $\mathbb{CP}^2$,$\mathbb{HP}^2$ and $\mathbb{OP}^2$ with respective principal orbits $G/K$ theWallach spaces $SU(3)/T^2$, $Sp(3)/(Sp(1)Sp(1)Sp(1))$ and$F_4/\mathrm{spin}(8)$. Almost all the Ricci-flat metrics constructed havegeneric holonomy. The only exception is the complete $G_2$ metric discovered in[BS89][GPP90]. It lies in the interior of the 1-parameter family on$\bigwedge_-^2\mathbb{CP}^2$. All the Ricci-flat metrics constructed haveasymptotically conical limits given by the metric cone over a suitable multipleof the normal Einstein metric on $G/K$.

Invariant Ricci-flat Metrics of Cohomogeneity One with Wallach Spaces as Principal Orbits