The sentence in the title supposedly means something like
「あなたの技術を見せてもらうかな」
I roughly understand what this sentence means as a whole but i'm having trouble parsing it.
I know that お手並み拝見 means: let's see what you've got; show me what you've got... accroding to jisho dictionary but i can hardly understand how it's used, example sentences show that it's ususually followed by the particle と so i'm guessing this て is another form of と ?
I also do not seem to understand what the ところ is doing here.