Lightly butter 13x9-inch glass or ceramic baking dish.
In medium saucepan, combine milk and cream. Cook over medium heat until bubbles just begin to appear around edges; remove from heat.
In large bowl, whisk together eggs, 2 egg yolks, sugar and salt. Slowly add milk mixture, whisking constantly. Whisk in 1/2 cup of the peanut butter and vanilla.
Spread remaining 1/2 cup peanut butter over one side of the bread slices; arrange in baking dish, peanut butter side up. Pour egg mixture over bread (slices will float).
Cover and refrigerate 1 hour. Heat oven to 350°F Place baking dish in large roasting pan or broiler pan; pour hot tap water into roasting pan, almost halfway up sides of baking dish. Bake 45 to 55 minutes or until top is puffed and knife inserted in center comes out almost clean. Let stand 30 minutes; serve warm.
Meanwhile, melt butter in heavy small saucepan over low heat. Stir in brown sugar and liqueur; cook 2 minutes or until brown sugar dissolves. Remove from heat; let stand 1 minute to cool slightly.
Whisk in 2 beaten egg yolks. Return to low heat; cook 4 to 5 minutes or until mixture coats back of spoon, stirring constantly. Strain through fine sieve, if necessary. Serve warm sauce over pudding.