Can I cook Brussels sprouts in a pan?
You can, but the surface-to-mass ratio means that the outer layers will overcook well before the inside is cooked, so unless you're interested in that texture, your two main options are:


Steam them (add some liquid, then put a lid on it)
Cut them smaller.  (halve or quarter before you saute)


I tend to halve smaller ones, and quarter larger ones, cutting through the stem each time so they don't fall completely apart while cooking (after trimming a little off the stem if it's showing signs of drying out).  Then saute 'til the outside has browned a little bit, and hit with salt and whatever spices (or bacon ... dice up some bacon and render the fat while you cut up the sprouts, then use the fat for cooking the sprouts)