How to cook 1.5+ inch veal steak to medium? It's a NY Strip part of a 12 month old calf. Hasn't been dry aged but I keep it 5 days in olive oil in a fridge. It has a bit of marble but way less than usual steaks could have. Pieces are pretty thick, 1.5 or more inch. 

I was thinking searing them 2 minutes each side on high heat - say 7/10, both sides, then also sear the side edges. Then putting in the preheated oven on 400F for 10 - 15 minutes. 

I don't have a thermometer to check so I'd need to be on the safe side that it's cooked, but also wouldn't like it to be well done.
Go buy a thermometer. There is no possible way to be guaranteed to hit the perfect point where it is medium well done but not overdone without knowing the internal temperature. How quickly it cooks depends on things like the temperature in your oven (they are rarely precise), the exact thickness of the steak, its exact internal temperature when you first place it in the oven, and so on. You can find a functioning oven thermometer for $3-4 at your local super market, so there is really no reason not to buy one.