Undecidability of TMs recognizing a decidable language The language $L = \{ \text{M} \mid \text{M  is a TM and the set of words w such that M halts on w is decidable} \}$ is given.

I need to prove that $L$ is NOT Turing recognizable. I've got a hint: it should be similar to prove to the Rice Theorem, using a reduction. However, this hint isn't very helpful to me.
Given a machine $A$, construct a machine $M$ which on input $x$, acts as follows: run $A$ on the empty input, and if it ever halts, run the Turing machine encoded by $x$ on the empty input.

If $A$ halts on the empty input then the language $M$ recognizes is the halting language, while if $A$ doesn't halt on the empty input then the language $M$ recognizes is the empty language.