Welcome to the community. I don’t think this can be done out-of-the-box. I am wondering what other information of your (templatized) board(s) you want to associate with the parent pulse.
Our Rollup Multiple Boards app allows you to create down-level boards based on templates. During the creation of the down-level (or you can call it templatized) board(s) the parent item maintains the connection with the board that has just been created. Then you can add recipes to report (for example) the sum of a number column in the templatized board, or the average etc. etc. For reporting the average the solution count the items in the down-level board(s) zo it is easy to make a little change to this app to report that too.
The reason why I am asking what other information you might want to see is that the solution might be a little top heavy for “just” getting the count.
Let me know if you want to discuss further.