Let $k$ be a field and let $T$ be an indeterminate. The "points" of $\mathbb{A}^1_k=\mathtt{Spec}(k[T])$ for the etale topology are given by the strict Henselizations of the usual local rings $\mathcal{O}_{\mathbb{A}^1_k,\mathfrak{p}}=k[T]_{\mathfrak{p}}$, $\mathfrak{p}\in\mathbb{A}^1_k$. I'm thus interested in an "hands-on" description of $k[T]_\mathfrak{p}^{\text{sh}}$, if there is one.
I'm open to assume that $k$ is a subextension of $\mathbb{Q}\subset \mathbb{C}$, if it helps to obtain an "explicit" (whatever it means) description.
I'm actually interested in the ring $k[T,T_2]\otimes_{k[T]}k[T]_\mathfrak{p}^{\text{sh}}$, so an "explicit" (whatever it means) description of the latter would also do.