The first question I would have is does the Browning have the same kind of medium burning powder restrictions like the M1 Garand does. If so, you'd want to select a powder like H335, IMR 4895, 4064, or 4320 for loading. With any of these powders, something about 46-50 grains would be appropriate for a 165 grain bullet.
My Garand likes Remington's 150 grain soft point with 47 grains of IMR4320.