I read this about 14 years ago, so forgive the lack of details...
Set in the late 1800s. The detective is Sherlockesque. He is a (I think rotund) Scottish man. Ex-Scotland yard turned private detective or a least has some police training. With a young handsome Jewish valet and young doctor does join him as a partner. He has a shooting range in the basement. And stone Roman bath in the back.
I’ve always wanted to re-read and figure out if there is a series. Good luck and thank you for your help!