Spray 6 mini Bundt pans with non-stick spray and set aside.
In a large bowl, mix together almond milk, water, melted butter, sugar and yeast and let sit for 5 minutes. Mix the flour and salt in stand mixer fitted with a dough hook. Turn machine to low and slowly add the liquid to the flour mixture. After dough comes together, increase speed to medium and mix until dough is shiny and smooth, 6 to 7 minutes. Turn dough onto lightly floured counter and knead briefly to form smooth, round ball.
Place dough in greased bowl and cover the bowl with plastic wrap and place in a warm area until it doubles in size, 50 to 60 minutes.
While the dough is rising, mix brown sugar, cinnamon and mini chocolate chips together in a bowl. Place melted butter in second bowl. Set aside.
Gently remove the dough from the bowl, and pat into a rough 8-inch square. Using a bench scraper or knife, cut dough into 64 pieces.
Roll each piece of dough into a ball. Working one at a time, dip the balls into the melted butter, allowing excess butter to drip back into the bowl. Roll in the brown sugar mixture, then layer balls in the muffin tin or mini Bundt pan, staggering seams where dough balls meet as you build layers. Once filled, let the unbaked dough rest for another 45 minutes.
Preheat oven to 350 degrees F. Bake until the top is deep brown and caramel begins to bubble around the edges, about 25 minutes. Cool in the pan for 5 minutes, then turn out onto a platter and allow to cool, about 10 minutes.
While the monkey bread cools, whisk the confectioners' sugar, almond milk and vanilla bean paste in a small bowl until the lumps are gone. Using a whisk, drizzle the glaze over the monkey bread, letting it run over top and down the sides of the bread. Serve warm.