This is not a breed, it is a mix
Not saying anything against mixes, I have 2 myself, but to go looking for someone who intentionally mix-breeds is, in my mind, only giving strength to the many irresponsible breeders already on the planet. Mixing one breed with another does nothing to "improve" EITHER breed - it simply mixes the two. The result may be perfectly lovely dogs, but they are not a breed. Yes, I understand that all modern recognized breeds were originally created by people, but don't ya' think we have enough at this point? Surely there are enough dogs are there looking for homes that you can find one that suits you!
Now, if you're looking for a dog with the size & temperament of a bullmastiff but with less drool & snoring problems, you might want to (1) contact a variety of REPUTABLE bullmastiff breeders and ask how their dogs are in this department; (2) look for other, similar breeds (some english mastiffs are not being bred to humongous size and retain enough muzzle to have better airflow); or (3) check out your local rescues or Petfinder and see if there's a mix out there you can adopt.