In a pot on the stove, pour in water, the butter, sugar and salt. Once it boils, pour in the flour all at once and stir intensely and patiently. When you get a homogeneous dough, transfer it into a bowl and let cool.
Then while stirring nonstop, add the eggs one at a time, beating well after each. As soon as the dough is elastic, it's ready. Pour the dough into a pastry bag with a medium nozzle and squeeze out the eclairs onto a large tray with baking paper.
If you get tips, smooth them out with a wet finger, to prevent burning when baking. Leave them to bake for 15-20 minutes in a 428°F (220 °C) oven. Do not open the oven - when ready, turn it off and let the eclairs cool in it, with the door slightly opened.
Remove the eclairs from the tray and let them cool completely.
Carefully pierce the bottoms of the eclairs with the tip of the pastry bag. Fill them with the softened ice cream (leave for 30 minutes in the refrigerator before working with it). Fill the eclairs and work quickly, so the ice cream doesn't melt.
To make the caramel syrup, caramelize the sugar in a pan on the stove and add the cognac and cream while stirring. Remove from the heat. Pour the syrup over the eclairs and keep a cool place for a while before you serve.