Preheat your oven to 350F and lightly butter/spray or line 2 muffin trays (enough for 14-16 muffins) with liners.
In a large mixing bowl, whisk together the flour, baking powder and soda, salt, and cinnamon.
In another mixing bowl, mash the bananas with a potato masher or fork till they're completely mashed and liquidy. Whisk together the non-dairy milk and vinegar or lemon juice, then add it to the banana mixture. Stir in the melted butter, sugar, and vanilla. Mix well.
Add the wet ingredients to the dry ingredients. Use a spatula or a whisk to mix the ingredients together well. The batter should be evenly incorporated; a few small lumps are OK, but there shouldn't be any flour visible. Stir in the chocolate chips.
Scoop the batter (using a muffin scoop or a 1/3 cup measure) into your prepared muffin tin. Bake the muffins for 22-25 minutes, or until just becoming golden at the edges. After 10 minutes, remove the muffins from the tin and allow them to cool on a cooling rack for 30 minutes before enjoying.