Nobody is standing between the House and senate doing whatever the heck they want to on this. They have been investigating, and Congress is one of the primary sources of accusation. See Schiff, Warner and a handful of others. They don;t have to step aside for Mueller either. They can tell him to go to hell, we have this.
What Congress can;t do is bring criminal charges. That's the line. But they can do all the investigation their little hearts desire. The regulation of that is election, fifth amendment, fourth amendment.
-- This Trump thing also make it important IMO to clearly define the steps required to bring about valid impeachment (formal charges), or else we get prima facia conflict of interest and "guilt by accusation" as the Lying Left is trying to do here. --
The lying left is able to defeat any system. it is a waste of time and effort to constrain them with statutes, regulations, and rules. They can only be defeated with ridicule. They are not reasonable, they are irrational and outcome driven.
Judgment in Cases of impeachment shall not extend further than to removal from Office, and disqualification to hold and enjoy any Office of honor, Trust or Profit under the United States: but the Party convicted shall nevertheless be liable and subject to Indictment, Trial, Judgment and Punishment, according to Law. --U.S. Const. Art. I, Sec. 3, Cl. 7.OK, so for reasonable suspicion of an executive branch officer and to avoid prima facia conflict of interest, the House, not the DOJ, should investigate to see if there is probable cause for the House to impeach (bring charges).
If impeached, the Senate tries the case as they do any impeachment case.
If convicted, the officer is subject to the judgment of removal and DQ - nothing further. As you say, Congress cannot bring criminal charges against a federal officer
However, after conviction (removal not explicitly necessary), the federal officer may be subject to criminal liability under federal courts probably by the DOJ regardless of what branch he's from because at this point he's been convicted by Congress and the DOJ is the only valid prosecutor in federal court.