1. Fill a large bowl with water. Squeeze half a lemon into it and set aside.
2. Remove all tough leaves from the bottom of the artichoke leaving unscarred and tender leaves. Trim stem and peel with a pairing knife.
3. Slice off one inch of the top of the artichoke exposing all the leaves. Trim any pointy leaves with scissors.
4. Cut artichoke in half. Using a spoon scrape out the fuzzy part, or 'the choke' of the artichoke. Place prepared artichoke in lemon water, cut side down.
5. Heat a large skillet to medium high heat. Add 2 tablespoons of butter and 1 tbsp of olive oil. Remove artichokes from water bath and pat dry with a paper towel.
6. Place cut side down into hot pan. Do not touch. Allow to cook for 3-4 minutes before checking for desired color (golden brown). Remove to a platter and set aside.
7. Add remaining butter and olive oil to hot pan. Add onion and garlic. Saute until soft. Add wine and juice of half lemon. Scrape up all the bits of the bottom of the pan. Simmer wine mixture until reduced by half. About 5 minutes. Add chicken stock.
8. Place artichokes cut side down into the broth mixture along with a sprig of rosemary. Cover and cook about 15-20 minutes until fork tender.
9. Transfer cooked artichokes to platter, sprinkle with salt and pepper. Best served warm with french bread.
Optional Garlic Butter Dipping Sauce
1. Melt 2 tablespoons of butter and one clove of garlic in a sauce pan or microwave. Allow to cool for 5 minutes. Drizzle over prepared braised artichokes before serving.