Preheat the oven to 350°F and adjust the rack to the middle position. Grease a bundt pan liberally with melted butter to ensure that the entire pan is well-coated. Set aside.
Place the eggs and brown sugar in the bowl of a stand mixer. Mix on medium-high speed for 4-5 minutes until the mixture is paler in color. With the mixer running on medium speed, slowly add the cooled butter, coconut milk, Meyer lemon zest, juice and the vanilla extract. Mix until incorporated.
In a large mixing bowl, whisk the almond flour, coconut flour, baking powder, baking soda, and salt until combined. Pour the egg and sugar mixture over the flour mixture and fold until incorporated. Add the poppy seeds and fold until incorporated into the batter.
Pour the batter into the prepared bundt pan and bake for 45-50 minutes until the cake is golden brown and a cake tester inserted into the cake comes out clean. Cool completely in the pan on a wire rack, then invert onto a plate.
To make the glaze combine the confectioners' sugar, coconut milk, Meyer lemon juice and zest in a bowl and whisk until combined with no chunks of sugar remaining. Pour the glaze directly over the cooled cake or drizzle over the cake with a spoon. If the mixture is too thick to pour add more coconut milk 1 tablespoon at a time until the icing is pourable.