Heat the milk and butter in a medium-large saucepan over medium-high heat
When the mixture simmers and the butter is melted, add the flour, salt, and pepper and stir well with a wooden spoon
Reduce heat to medium and stir for 2 minutes to dry the mixture out
Turn off heat and continue stirring for another minute to continue to cool the mixture
Add the eggs 1 at a time, beating well to incorporate each egg before adding the next
Mix the batter until it is very smooth
Transfer the mixture to a pastry bag with a large plain tip
Pipe the mixture onto a parchment lined sheet tray in rows, about 1 inch in diameter, and 1 inch apart (If you notice any bumps, dip your finger and flour and gently smooth the surface of the dough)
Bake for 10 minutes
Reduce the heat to 375 degrees
Continue baking until golden brown, about 8 to 10 minutes more
Remove from the oven and allow to cool
Beat the goat cheese, cream, salt in a medium bowl using an electric hand mixer on medium speed until light and fluffy, 1 minute.
Transfer the whipped goat cheese to a pastry bag fitted with a plain tip and refrigerate until ready to pipe into the gougeres.
With a paring knife, cut the top from each gougere, leaving either attached slightly (like a hinge), or remove. Pipe about 1 1/2 teaspoons of the whipped goat cheese into the center of each gougeres and replace the tops.