Preheat your oven to 350°F (175°C). Grease an 8x8 inch baking pan and line it with parchment paper, leaving an overhang on two sides.
In a saucepan over low heat, warm the milk, butter and chopped chocolate, stirring constantly, until melted and smooth. Do not let it boil. Remove from the heat, whisk in the sweetened condensed milk and vanilla, and let cool for 5 minutes.
In a large bowl, whisk the glutinous rice flour, sugar, cocoa powder, baking powder and salt, breaking up any cocoa lumps. Make sure you use glutinous rice flour, as regular rice flour will not give the chewy texture.
Pour the chocolate mixture into the dry ingredients and whisk until completely smooth and glossy. The batter will be thin and pourable, which is exactly right.
Pour the batter into the prepared pan and sprinkle the chocolate chips on top. Bake for 40 to 45 minutes, until puffed with a crackly top and edges pulling away from the pan, and a toothpick comes out mostly clean (a little stickiness is normal).
Let the brownies cool completely in the pan, at least 2 hours. This is important, because the signature chewy, bouncy texture develops as they cool.
Lift them out and cut into 16 squares, lightly oiling between cuts to prevent sticking. Store airtight at room temperature for up to 2 days, since the fridge makes mochi firm.