How to Make It
Pull off the outer leaves of the artichokes until you reach the pale green hearts. Cut off the top third of each of the small artichokes; cut off the top two-thirds if using larger ones. Cut off the stems and trim the leaves around the base. Leave the small artichokes whole; scoop out the chokes from the larger artichokes and halve or quarter the trimmed bottoms. Transfer them to a bowl of cold water mixed with the juice of 1 of the lemons to prevent browning.
Warm 3 tablespoons of the olive oil in a large nonreactive saucepan. Add the artichokes, garlic, salt, pepper, thyme sprigs and the juice of the remaining lemon. Pour in 3/4 cup of water and bring to a boil. Reduce the heat to low, cover tightly and braise gently until all the water has evaporated and the artichokes are tender, 15 to 20 minutes. Season the artichokes with the remaining 2 tablespoons olive oil and serve warm.