Once the ExtendedReport extension has been added, there will be additional reports shown in the CiviReports section. To be able to use one of these as a block, go to Administer -> CiviReport -> Create New Report From Template and then find the Extended report you want and click on that report. The next screen it takes you to is the important one. You can make amendments to the report there and you must go to the Display Options tab and select "Make available for contact summary page (requires contact layout editor extension)", then refresh the results and then view the output. Next, you have to use the Actions dropdown to "Save a copy" and call it the name of the block you want to appear in the Contact Layout Editor.
Once you have done this, the block will appear in Contact Layout Editor (you may have to go out and back in to the Contact Layout Editor for this to show) and then you can drag it in as you can the other blocks.