Baking bread/cake yields different results than expected
Assuming this is actually a recipe that worked for your friend (it does seem pretty weird - see rumtscho's answer)...


  We are both using a soup spoon, not a measured one, Yet we get different results.


That's exactly why you got different results. Your soup spoons aren't necessarily the same size.

You need to use some kind of reliable, standard measurement when baking, especially for leavening (like the baking powder), whether it's real measuring spoons, or a scale to measure by weight. If your friend can't provide you with a recipe using reliable measurements, then you won't be able to reliably reproduce it.

From your description ("condensed and hard" not "fluffy, light"), it could be that you've used less baking powder than they did, or more tahini than they did. So even if they can't give you a good recipe, you may be able to experiment on your own to find one. But if you do that, do yourself a favor, and get accurate measuring spoons or a scale.