Prove “almost clique” is NP complete

Question

Given $G=(V,E)$, undirected graph, a group of vertices $S$ is called almost clique if by adding a single edge, $S$ becomes a clique.

Consider the language: $L=\{\langle G,t\rangle \mid \text{the graph \(G\) contains a \(t\)-sized almost-clique}\}$. Prove that $L$ is NP-complete.

Obviously, it is solved by polynomial reduction, but is it from Clique or 3SAT? And how?