  We construct a continuous 1-parameter family of smooth complete Ricci-flat
metrics of cohomogeneity one on vector bundles over $\mathbb{CP}^2$,
$\mathbb{HP}^2$ and $\mathbb{OP}^2$ with respective principal orbits $G/K$ the
Wallach 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 have
generic 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 have
asymptotically conical limits given by the metric cone over a suitable multiple
of the normal Einstein metric on $G/K$.
