Sift the flour 2-3 times through a fine sieve. Wash the chicken eggs. Cut the butter into cubes and leave to soften at room temperature. Preheat the oven to 180-190 degrees and line a baking tray with baking paper.
Make a simple choux pastry. Bring water and oil to a boil over medium heat. Add salt and stir. Add flour little by little, stirring continuously to avoid lumps forming. Remove from heat and cool slightly. Beat the eggs, adding them to the dough one at a time.
Make homemade eclairs. Place the dough into a pastry bag and form small strips on the baking sheet. Place the cakes in the oven and bake until golden brown, about 30-40 minutes.
Prepare the chocolate sauce. Grind the chocolate in a blender until fine crumbs. Pour cream, corn syrup, and sugar into a saucepan. Place over low heat and, stirring continuously, bring to a boil. Pour the hot cream mixture into a blender with chocolate, add vanilla and butter. Stir until smooth.
Fill the eclairs. Cut the eclair in half lengthwise and fill it with a small amount of ice cream. Fill all the cakes this way.
Pour chocolate sauce over the eclairs and serve.