Turing Machine That Accepts Machines With Undecidable Languages
The language you are describing is called an "index-set", which means that it is accepting languages, rather than machines specifically. More formally, if we have two machines $M_1, M_2$, and $L(M_1) = L(M_2)$, then $M_1 \in Undecidable \iff M_2 \in Undecidable$.

There's a theorem called Rice's Theorem that says that index sets are always undecidable. The proof on the Wikipedia page shows how you can reduce the halting problem to any index set.