Preheat the oven to 350ºF. Position an oven rack to the upper and lower third positions.
In a bowl, whisk together the glutinous rice flour, ginger, salt, and baking powder. Set the bowl aside.
Snap the brown sugar slabs into smaller sections and place them into a saucepan. Pour the water into the saucepan. Cover the saucepan with a lid, and bring to boil. Reduce the heat to medium.
Use a wooden spoon or spatula to break up the remaining pieces of brown sugar so that they dissolve faster. Cover the saucepan with the lid again and continue simmering until the sugar slabs dissolve completely, about 3 to 5 minutes. (See note 4 if using granulated dark brown sugar)
Remove the saucepan from heat. Pour the can of coconut milk into the saucepan. Then, add the butter slices and stir until the butter melts. The cold temperature of the butter will help chill the liquid a little faster. Let the sugary liquid cool for 10 to 15 minutes, until it is slightly warm (about 110ºF to 120ºF).
Whisk the eggs in a small bowl and then mix them with the other wet ingredients. .
Gradually add the warmed sugary liquid to the dry flours (I added the liquid in 2 additions). Mix the dry and wet ingredients together, until there are no more streaks of flour, about 1 to 2 minutes.
Use your spoon or spatula to flatten large lumps of flour by flattening them against the sides of the bowl. Give the batter a quick stir again. There’ll still be lots of smaller lumps of flour in the batter, and that’s completely fine.
Grease the muffin pans with cooking spray. Use a brush to ensure that the sides of the wells are covered with oil too.
Fill each well of the muffin pans until they’re about 80% full (see note 5). Sprinkle sesame seeds over the batter.
Bake the nian gao for 30 to 32 minutes, switching the positions of the muffin pans halfway. The edges of the nian gao should be deeply golden, like the color of ginger snap cookies. If you are using a dark gray muffin pan, the nian gao should be ready in about 30 minutes. If you are using a pan with lighter color metal, they’ll need a few more minutes.
Remove the nian gao muffins from the oven and let them cool in the pan for 5 to 10 minutes. The cakes will deflate as they cool.
Transfer the nian gao to a cooling rack and let them cool for another 20 to 30 minutes before eating. The edges crisp up more as the cakes cool.