Preheat oven to 350 degrees F. Spray a 9x5-inch loaf pan with cooking spray.
Place the butter in a large, microwave safe bowl. Melt the butter in your microwave. (Or, you can melt the butter in a pot on the stove.)
Add the sugar, mashed banana, eggs, milk and vanilla to the bowl with the melted butter. Whisk to combine.
Add the baking soda and salt to the bowl with the wet ingredients. Whisk until well combined.
Add the flour to the bowl. Use a rubber spatula to mix until just combined. Be very careful not to overmix. Fold in 1/2 cup of the chocolate chips.
Melt the remaining 1/2 cup chocolate chips, either in a glass bowl in the microwave or in a small pot on the stove. Add 1 cup of the banana bread batter to the melted chocolate and stir until combined.
Spoon the chocolate batter alternately with the plain batter into the greased loaf pan: first put half of the plain batter in the pan, followed by half of the chocolate batter, and repeat. Use a knife to swirl the two batters together. Sprinkle a few extra chocolate chips on top of the loaf, if desired.
Bake for 55-60 minutes, until a tester inserted into the center of the bread comes out with just a few moist crumbs attached. Check on the bread at 35 minutes and loosely cover with a piece of foil to prevent the top from over-browning.
Place the pan on a wire rack to cool for 15 minutes. Remove the bread from the pan and let cool completely on the wire rack.
Notes
Store banana bread at room temperature for up to 5 days or in the freezer for up to 3 months. Cool bread completely before freezing.