How to update IRA shares vs brokerage shares

The very best way, in my opinion, is to work through the transaction history in Quicken, compare that to the transaction history in ML, and enter/change transactions in Quicken to get the final totals of share sand cost basis to agree.

If you just established the IRA in Quicken and did an initial download of transactions, understand that it's highly unlikely that first download sent you all the transactions that have occurred in that account if the account hasn't been opened "recently."  The financial institution holding the account - ML here - controls how far "back in time" transactions are available to download into Quicken, so the differences in shares might easily pertain to transactions before the date associated with the oldest transaction downloaded.

If you don't want to do the work to get all the transactions into the Quicken Account there are the "Add" and "Remove" actions you can enter to get the numbers to agree.  The easiest way to do that is to select the "Update share balance..." menu item that's available when you click the gearwheel in the upper right hand corner.  If ML has the basis figures (in total) for each security then I'd advise the manual Add/Remove actions; those actions allow you to enter an "acquired date" AND basis.  That way your share numbers and total basis will agree to ML, although the "details", i.e., "lot" information, will differ.