"option to break after 12 months with at least 2 months’ notice"
In my opinion, the sentence above can be interpreted as follows:
1) the agreement can be broken at least 12 months after inception date. In our case, the agreement starts June 1st 2019 and hence the agreement cannot be broken before May 31st 2020.
2) Would we wanna break the agreement, we need to give a 2 months notice before ending the agreement. Example: if we wanna leave Sept 1st 2020, we need to inform you/the landlord latest June 31st 2020.
Both conditions 1 and 2 have to be fulfilled. The two conditions are inclusive.