"Would tomorrow between 11:30-12 work for me to give you a call?" Meaning?

The caller is asking whether it would be convenient to you (as the proposed recipient of the call) to be calleis d by the person adking the question somewhere between 11:30am and 12:00 am.

The reason they are saying "...convenient for me to give you a call" is that they actually mean "Would it be convenient if I gave you a call..?" They are not asking whether it would be convenient for them, they would know that.

The phraseology is quite poor and somewhat unclear but this sort of convolution is quite common in normal speech. If they had actually said "Would it be convenient for you if I gave you a call between 11:30 and 12:00?" You would not have a problem and would not, unless you responded negatively and asked them to call earlier, expect call at 10:30