Preheat the oven to 350°. Line a 10-inch deep-dish pie plate with foil. Spray the foil with vegetable oil spray.
In a large saucepan, melt the butter with the semisweet chocolate over low heat, stirring occasionally. Remove the saucepan from the heat and whisk in the sugar, cocoa powder and salt until smooth. Whisk in the eggs one at a time. Add the flour and whisk until just blended. Pour the batter into the prepared pie plate and bake for about 25 minutes, until the top is shiny and the center is set. Transfer the pie plate to a wire rack and let cool completely.
Scoop the coffee ice cream into balls and arrange them in a single layer on top of the brownie pie. Scoop the chocolate-chocolate chip ice cream into balls and arrange them on top of the coffee ice cream. Drizzle all over with the caramel and hot fudge sauces and freeze for at least 4 hours, until firm.
Just before serving, set the pie plate on a warm towel. Lift out the pie and transfer it to a work surface. Peel off the foil, cut the ice cream pie into wedges and serve.
The pie can be frozen in an airtight container for up to 1 week.