How to talk to an intimidating professor?
This is coming from someone who worked and still works with the most intimidating professor in our lab. This professor was my teacher when I was a bachelor student and he was also my supervisor project for my Master degree (And that's when I developed my fear). Now he is one of my co-supervisors for my PhD. I never approached him until this year (5 years to overcome my fear). So all this just to tell you that "I know :)".

The year I approached him, I discovered the following information (and the mistakes I made):


The professor was just professional: strict when it comes to deadlines and assignments, meetings were heavy and only work-oriented (a lot of information, a lot of tasks to do). This was stressful to a lot of students.
The professor is seriously passionate, so he takes everything to the next level. You really should arrive to class punctually, no small talks, stay focused. You break the rules, you leave.  
I kept hearing past stories, or bad experiences, from other students and let those experiences affect our professor-student relationship. 
And mostly, I missed many opportunities by not taking the first step in the past.
I made the mistake of mixing "How he does his job" with "Who he is".


So here is the only answer I have to your question: Just do it, I am sure that this intimidation is just in your head. I even noticed that I can easily start these off-class relations with other professors, but never with him. So here is something I would do: 


I will schedule a meeting by sending an email (my professor was the Head Of our Lab, he is always busy). I will say that I need a recommendation letter for example.
During the meeting, introduce yourself and why you need the recommendation letter and try to start a conversation from there. Tell him your future plans, and ask for his opinion. He is your professor after all, his job is to guide you :).
During class, be active and always be interested. You can not earn his respect if he does not see how passionate you are.
Always take the first step. And if doesn't go your way, it's okay. As Buffy said, take it easy, you have a lot of time and "several opportunities to reinforce any interest"


Good luck.