Can I upgrade my Specialized Epic Comp 29er 2x10 to a 1x11?
Yes, it can be done, but you should consider what the cost of the components and  tools or paying for installation would be vs a whole new bike.

You will indeed need a new crank, cassette, rear shifter and chain. May as well replace cables and housings at the same time.

If you have and will stay with Shimano, you might be able re-use the rear derailleur, as Shimano MTB 10 and 11 speeds use the same cable pull ratio, I believe. You just need to check that the derailleur can accommodate the largest sprocket size you will be using.

Unlike road systems, 11 speed MTB cassettes fit on 10 speed wheel freehubs as the largest sprockets can overhang the drive side flange and sprockets a little.