With an electric mixer beat the eggs until tripled in volume and fluffy, about 5 minutes. Add a shot of Baileys and continue to mix until just combined.
Remove the lid and seal from Nutella jar and microwave for 30 seconds to soften. Pour Nutella into a large mixing bowl. Fold the egg mixture gently with a spatula into Nutella, one-third at the time.
Transfer into a greased 9" round or square baking pan. Bake for 20-25 minutes, or until top is set.
Baileys caramel sauce (optional)
Put the butter, sugar, and salt in a saucepan. Heat over medium heat until the sugar melts and turns golden brown in color, stirring occasionally. Remove the pan from the heat and add Baileys (sugar will harden). Return to the stove and cook, stirring as needed, until the sugar melts and combines with the Baileys to make a thick caramel.
Add milk or cream as needed, until you have thinner sauce. The sauce will thicken significantly as it cools. Let cool at room temperature. Refrigerate the unused sauce. Reheat as necessary and add more milk until you have pliable consistency.
To serve, top the brownie slices or squares with ice cream and drizzle with sauce.