Two 2x12 will not span 28’ with a load on it, 3 might tho. Assuming you can even find 2x12 28’ long. They would need to be Ponderosa pine, Southern Yellow pine, or Douglas Fir to even consider it. I would assume that you want to cut all of the vertical supports to about 1’ from the top to leave the radius of the roof intact ant the eaves, and rest them on top of the header. A shoe on those would probably be necessary to mount them to the beam, you could probably fab that to go inside the down drop of those legs, use a pass through bolt to hold them to the leg, mount a plate on the bottom and fasten them through the header by drilling holes in them for screws. If you don’t mind a post in the span, then yes, 2 would hold the span with a post. You will still need SYP, Ponderosa or Doug Fir as you will not find regular SPF 2x12 that long. With a post you wouldn’t need one long piece, you could use 14’ lumber and join them on top of the post.
I myself would use 2 16” LVL’s, I believe they would free span the entire 28’. 2) 18” LVL definetely would.