Preheat the oven to 350°F (175°C). Line a 9 x 5-inch bread pan with parchment paper, letting the paper extend up the long sides, and spray the pan with nonstick cooking spray.
Scoop ice cream into a large measuring pitcher or bowl and press to measure 3 cups. Let the ice cream melt until pourable.
Place the self-rising flour in a mixing bowl. Pour the melted ice cream over the flour and whisk until the batter is smooth and evenly combined.
Stir in about 1/3 cup of the mini chocolate chips into the batter, reserving the rest to sprinkle on top.
Pour the batter into the prepared pan and evenly smooth the top. Sprinkle the remaining mini chocolate chips over the batter.
Bake on the center rack for 50–60 minutes, or until a toothpick inserted into the center comes out clean.
Cool the bread in the pan for at least 15 minutes, then lift it out using the parchment paper. Cool completely on a rack before slicing and serving.