Can Views be used to create block menu of taxonomy terms associated with a content type along with a count per term?

Hello,

I have a content type “Technical Articles” and have created a taxonomy for Technical Article Categories which has categories and subcategories (parent/child). I would like to create a block (to be displayed on the landing page for all technical articles) which will display “View By Category” list of all terms in the Technical Articles taxonomy with numbers next to each category and/or subcategory and when a category/subcategory is selected on the left, all articles for that category will be displayed on the right. Can this be done with Views? Example screenshot of desired end result is attached (count is missing next to each category). I have tried, but have not been successful; an export of my sample view is also attached.

Any assistance is greatly appreciated.

Thank you