No, always boil. I've done bubble & squeak with them but it hasn't been a success (the sprout part was fine, but getting the patty brown without gluing to the pan never worked so they wound up as mashed potato with sprouts).
I think a lot of it is in the prep. Yesterday I was at Xmas dinner with the inlaws and - horror - someone else prepped them. What seems to be the way to do them is to cut off the stem and that removes some leaves and you're done. By the way I do them is to peel the leaves until there is no shadow of a previous leaf (and in doing this you notice where they are decomposing, which you don't when it's done the other way). Once the main part is OK, cut the stem to suit. Takes three times longer but the results are perfect.
Done my way the prepped sprouts look like your middle photo. Done other's way they look like the other photos. I think the outer layers, the darker green leaves, apart from hiding stuff also taste different.
Cooking: throw them in a pan, cover with water, teaspoon of salt, turn on the heat. Once boiling, leave for 10 mins then test - a fork should go through reasonably easily and consistently. If they are underdone (chewy) you'll feel a bit of extra resistance as you hit the middle. Overdone and there won't be any resistance at all - use these for bubble & squeak practice.
Done right you can shove any excess in the fridge and they are still good the next day when cold. And the day after. Never had any last longer than that so can't say about third day.
Edit: sorry, got carried away
The chewy thing, as you've probably figured, is when the middle hasn't cooked long enough. There's a pretty short window between the middle being under done and the outer being over done. One way around that for baking and the like is to cut them up, perhaps halving will be sufficient. Or shred them - I've shredded and then stir fried raw sprouts with bacon and they were OK. More or less. Prefer boiled though