Preheat the oven to 400°F. Line 2 baking sheets with parchment paper.
In a medium saucepan, heat butter, milk, sugar, and salt over medium heat until it boils. Add flour and stir well. Return to heat and stir until the dough forms a skin and pulls away from the pan.
Transfer dough to stand mixer and beat for 1 minute. Add eggs one at a time until fully incorporated.
Pipe dough onto the baking sheet into 4-inch logs. Bake for 25–30 minutes at 400°F, reducing temperature to 350°F after 10 minutes. Let cool.
For the filling, mix milk, condensed milk, pudding mix, and vanilla bean paste. Whip the cream with remaining condensed milk and fold into the pudding.
Pipe the filling into the cooled eclairs using a piping bag.
For the glaze, melt chocolate and heavy cream. Dip the tops of the eclairs into the glaze and let set for 20 minutes.