I've bought a rolled breast of lamb and was wondering how to cook it.

I was thinking of browning it in a pan on all sides then transferring it to the slow cooker for several hours with some root veg and stock.

The alternative is brown in a cast iron pan and then stick the pan in the oven for an hour or two.

Any suggestions?

Yum. I would slow roast in the oven. So the fat renders out and you'll get this most tender-falling-apart meat.
Rub it in first with seasoning and herbs like thyme and rosemary.

Salivating now !

I practically lived on breast of lamb when I was pregnant. Laid it flat on a bed of root veg and cooked it long and slow in the oven. There is nothing quite so delicious as crispy lamb fat.

I sometimes have mine cooked in marinade sauce.

The last two times I cooked lamb (within this month) it was lamb shanks and a leg of lamb.
I browned both as best I could.
The shanks went in the slow cooker on low for five hour or more - they slid off the bone.
The leg went in the oven at 160 for seven hours covered in foil to start and was meant to be pulled apart with forks consistency.
My wife got impatient whilst I was out because she needed the oven and knocked it off after five hours or so.
It wasn't totally "pull apart" but was still incredibly tender.
Here's a recipe from Huge Furry Whippingstool
http://www.goodtoknow.co.uk/recipes/...l-s-roast-lamb

In the end I combined both methods.

I browned the lamb all over and transferred it to the slow cooker.
I then sauteed carrots, swede and onions with herbs, seasoning, and red wine.
I added that to the slow cooker and did a final deglaze with chicken and lamb stock.

Cooked it on low for 6 hours.

Marinade in Oloroso Sherry for a day
Paint with Orange Marmalade
Roast for the appropriate time.

And......?

Where did you get lamb stock?
I don't ask that snobbishly - you just don't see it on supermarket shelves.
I made some from my leg of lamb remains.

Knorr lamb stock cubes

If its already rolled I cook in the oven on a rack and tray (it will loose a lot of fat). Pierce the skin and insert slivers of garlic, Rosemary and enjoy. Flat breasts are good, use two or three and layer with stuffing of choice then roll and tie, cut into joints then roast. Cut into thin strips they will take a BBQ sauce and cook crisp on your BBQ (or very hot oven). Cut into strips it will make a good slow cooked stew but you'll need to skim off the excess fat.