Step 1: Prepare the Oven and Baking Sheets.

Preheat the oven to 400°F (200°C).

Line two baking sheets with parchment paper. This prevents the eclairs from sticking.

Step 2: Make the Choux Pastry.

In a medium saucepan, combine 1/2 cup of water, the cubed butter, milk, granulated sugar, and salt.

Place over medium heat and bring the mixture to a boil. Make sure the butter is completely melted.

Remove the pan from the heat.

Add the flour all at once. Stir vigorously with a wooden spoon until the flour is fully incorporated.

Return the pan to medium heat.

Stir continuously until the dough is smooth, forms a skin on the bottom of the pan, and pulls away from the edges of the pan, 4 to 5 minutes.

Stir in the vanilla extract.

Step 3: Cool and Beat the Dough.

Place the dough into the bowl of a stand mixer fitted with the paddle attachment.

Allow the dough to cool for 5 to 7 minutes. This prevents the eggs from cooking when added.

Beat the dough for 1 minute on medium speed. This helps to release some steam.

Step 4: Incorporate the Eggs.

Beat in the eggs, one at a time, scraping down the sides and bottom of the bowl after each addition.

Beat very well until each egg is fully incorporated before adding the next.

The dough should be smooth, glossy, and thick enough to hold its shape.

Step 5: Pipe the Eclairs.

Transfer the choux pastry dough to a zip-top bag with a 1/2-inch corner snipped off. Or use a pastry bag with a large round tip.

On one of the prepared baking sheets, hold the piping tip 1/2 inch above the parchment paper.

Slowly pipe logs about 4 inches long and 1 inch wide.

Stop squeezing and move the tip in a quick circular motion as you lift away. This avoids pointed ends.

If necessary, use a wet finger to smooth any points on the eclairs.

Repeat with the remaining batter and the second baking sheet, piping 8 to 10 eclairs per baking sheet. Leave space between them.

Step 6: Bake the Eclairs.

Bake the eclairs, one baking sheet at a time, until they are puffed and golden brown, 25 to 30 minutes.

Reduce the oven temperature to 350°F (175°C) 10 minutes into baking time.

Do not open the oven door during baking. This can cause the eclairs to collapse.

Step 7: Cool the Eclairs.

Cool the baked eclairs completely on a wire rack. This allows them to dry out and become crisp.

Step 8: Make the Filling.

In a large bowl, whisk together the whole milk, 1/2 cup of the sweetened condensed milk, the instant vanilla pudding mix, and the vanilla bean paste.

Whisk until well combined, about 2 minutes.

Allow the pudding to sit for 5 minutes to thicken.

In another large bowl, use a hand mixer to whip the cold heavy whipping cream with the remaining 2 tablespoons of sweetened condensed milk on high speed.

Beat until firm peaks form.

Fold the whipped cream into the thickened pudding mixture in 3 additions. Fold gently to combine.

Step 9: Fill the Eclairs.

Transfer the filling to a piping bag fitted with a 1/2-inch round piping tip (Wilton 1A).

Use a toothpick or the end of a chopstick to poke one hole into the bottom of each eclair.

Insert the piping tip into the hole. Pipe filling until the eclairs are evenly filled.

Step 10: Make the Chocolate Glaze.

Place the chopped chocolate in a medium heatproof bowl.

In a large glass measuring cup or another medium bowl, microwave the heavy cream until steaming, 45 seconds to 1 minute.

Immediately pour the warm cream over the chopped chocolate.

Allow to sit for 1 minute.

Whisk until smooth and glossy.

If the chocolate is not fully melted, microwave the mixture at 50% power at 15-second intervals, stirring until smooth.

Step 11: Dip the Eclairs.

Set a wire rack over a baking sheet. This will catch any dripping chocolate.

Dip the tops of the filled eclairs into the chocolate glaze. Only submerge the tops.

Let any excess chocolate drip off.

Set the dipped eclairs onto the prepared wire rack.

Step 12: Set the Glaze and Serve.

Allow the chocolate glaze to set before enjoying, about 20 minutes.

Store the eclairs in an airtight container in the refrigerator for up to 3 days. They are best enjoyed the day they are made.