Pour the milk into a small pot and bring it to a boil. Transfer it to a bowl and add the 3 tea bags. Let it infuse the milk and cool down.
Wipe out the pot and place it back on a medium heat. Brown the butter. Allow it to melt and then slowly become dark golden in color. It should become very foamy and the milk solids should be light brown. As soon as you reach this colour, transfer to another bowl (as it will burn quickly) and mix in the honey. Allow this mixture to cool down.
Sift the flour, baking powder, and baking soda through a sieve and add the salt, sugar, ginger, and cinnamon. Mix well to combine. Once the brown butter and milk have cooled, squeeze the residual milk from the teabags into the milk and discard them. Add the milk to the brown butter and honey mixture and mix well.
Mix the wet mixture into the dry ingredients, reserving a little bit in case the batter gets too thin. Mix well with a wooden spoon. Add the eggs and mix again until smooth.
Grease a 9x5-inch rectangular bread tin with a little bit of butter or oil. Pour in the batter. If the batter is more than an inch below the top of the bread tin, pour a little bit out to prevent it overflowing.
Bake for 1 hour and 10 to 20 minutes, or until a skewer comes out clean when pierced. Let the cake cool in the tin before removing it. It should rise in the oven and deflate slightly once cooled.