Preheat oven to 400 degrees.
PREP THE ARTICHOKES: Fill a bowl large enough to accommodate the artichokes when halved with water (about 2 quarts). Add the lemon juice. (I often toss in the lemon pieces.). As you trim and prep the artichokes, immediately immerse the artichoke in the lemon (acidulated) water. Remove the tough outer leaves from the bottom and stem of the artichoke. Trim approximately 1 inch from the top of each artichoke. Trim the tips of each leaf. (Be careful! They can have sharp barbs.)
Drain the artichokes by turning them upside down, then shake off any excess water. Cut the artichoke in half from top to bottom. Scoop the fuzzy choke from the center of each artichoke.
ROAST THE ARTICHOKES: Drizzle a large baking dish or roasting pan with olive oil. Season artichokes with salt and black pepper. Place 2 garlic cloves in each artichoke, top each with a sprig of thyme and rosemary, then place a lemon slice on each.
Carefully flip the artichoke half over so the cut side faces down. Ensure the garlic is securely inside so it doesn't burn during roasting. Drizzle with olive oil.
Cover the roasting pan with aluminum foil. Roast for 45-50 minutes or until tender. Test doneness by gently pulling on one of the leaves or test with a small, sharp knife. Roasting time will depend upon the size of the artichokes.
MAKE THE GARLIC BUTTER: Cut the butter into pieces and place in a microwave-safe bowl. Cover with a paper plate. Microwave on HIGH for 30 seconds. Stir, then place the paper plate back on top and microwave on HIGH for 10 seconds. Stir again. The time may vary with the wattage of your microwave. What you don’t want is for the butter to boil or separate. Mash the garlic to a smooth paste. Stir it into the melted butter. Alternatively, you can melt the butter in a small saucepan on the stovetop.
Mash the garlic to a smooth paste. Stir it into the melted butter.
Garnish with fresh herb sprigs and lemon wedges.