Preheat oven to 350° F. Line a 9x13-inch pan with parchment paper so that the paper overhangs the sides.
In a medium saucepan set over low heat, melt the butter and chocolate, stirring until smooth. Remove from heat and add the sugar. Add the eggs one at a time, mixing after each. Stir in the vanilla and mint extracts. Add the flour and salt and mix until no streaks of flour remain.
Pour batter into the prepared pan and bake until brownies are set and the top appears dry, about 25-30 minutes. Let brownies cool to room temperature, then place in the freezer for 1-2 hours.
Let ice cream sit at room temperature for about 5-10 minutes to soften. Remove brownies from the freezer and cut in half crosswise. Place one half back into the pan, top side-down. Spread softened ice cream evenly on top, then cover with the other half of the brownies, gently pressing down to make sure the brownies and ice cream are well sandwiched together.
Return bars to the freezer and let harden for 1-2 hours before slicing and serving. For easier slicing, use a knife dipped in hot water and wiped dry with a clean towel.