My brother-in-law says it's hard to get as much browning in an electric broiler and suggested I try sautéing again. So I did so with the intention of getting a nice golden brown and then finish cooking via poaching.

I decided to try to make a pan sauce of the poaching liquid with water, "better than bullion" chicken base, dried onion, thyme, bay leaf, clove, paprika and cheese.
The browning was done quite nicely, but I must have put too much of the chicken base in as the sauce was way too salty. Also, I've seen my brother-in-law twice add shredded cheese to a soupy dish and end up with a nice blended, thickened sauce contrary to what I would have expected. Well, what I expected happened to me: the cheese just globbed together and stuck to the pan, and once I gave up trying to stir the glob into the sauce I just threw away the cheese glob. Aside from the over-salt and cheese issues the sauce was nice enough to try again next time. I even used it on the chicken while cringing at the salt content.
The browned chicken was quite yummy, although I think I cooked the smaller breast more than I intended. It wasn't dry, but it wasn't as fabulously juicy as my broiled chicken has been. I think the bigger piece is slightly underdone, but it's for reheating later so that's okay.
Update: My brother-in-law laughed at me. The consensus is his liquids must have had a roux or other emulsion established before he added the cheese, so the cheese emulsified for him. In my attempt here there was no emulsifying agent.