AppStore require apps for iPhone and iPad to be build with iOS 13 SDK after June 30, 2020
Yes, that is entirely possible. It is just setting the target version to iOS 12 in the first version, and iOS 13 in the second version. You will have to set the iOS 13 release to be timed for release on 30th of June, but apart from that there's nothing "special" in this.

Note: It seems you might have mixed some things up. The deadline requirement for June 30th 2020 is just that the app is to be built with the iOS 13 SDK - it doesn't mean that you have to set your target deployment version to iOS 13. So you can definitely build with iOS 13 SDK to fulfill the deadline requirement, and still only require iOS 11 or iOS 12 or whatever you need. 

Users on iOS 12 (or even earlier) should have no problems running apps built with the iOS 13 SDK as long as the target deployment version is set accordingly.