Thanks! And, yeah, I hear you -- I'm new to this style of play/design, too. From the little I know, I'd say:
Broadly, whatever works for everyone at the table is the best way to handle specialization/expertise. A brief convo to confirm buy-in, then run with that ruling.
Specifically, I'd probably either go with rolling 3d10 and keeping highest two (advantage), adding a d6 to the 2d10 for the expert (gives some edge but still chance of failure), or a flat +5 to any related rolls (definite edge). Any of those could work (or other options), depending on how much of an edge you want to have in your game.
Hope that's useful! I'm still getting my head around it all, as well. Have fun!