You are going to be preparing the éclair dough in a pot on the stove. Start by heating the butter and water in the pot until it comes to a boil. Turn off the heat and stir in the flour. Turn the burner back on to medium and keep stirring until the mixture forms into a ball. Then turn off the stove and remove the mixture.
Allow the mixture to cool for about 10 minutes and then use a stand or hand mixer to incorporate the eggs one at a time into the dough.
When fully incorporated, Take heaping tablespoonful of the dough and place them on baking sheets (preferably on silicon or parchment paper). I tend to like rounds but if you want the traditional elongated form shape it into that shape.
Bake the éclairs at 425F for 15 minutes and then reduce the temperature to 375F and bake for another 15 minutes. Turn off the oven, crack the door open and allow the éclairs to cool slowly in the oven for another 30 minutes.
Chocolate glaze
In a pan over medium heat bring the cream and corn syrup to a boil, turn down the heat, add the chocolate and stir until the chocolate if fully incorporated. Remove from the stove and use a spoon to pour the glaze on the top of the éclairs.