Classic Potato and Cheese Pierogi

500 g russet potato, peeled and quartered

1 yellow onion, finely chopped

1 egg, lightly beaten

30 g unsalted butter, melted, for dough

60 g unsalted butter, divided

150 g cheddar cheese, shredded

120 ml sour cream, for serving

5 g salt

300 g all-purpose flour

180 ml warm water, about 40°C (100°F)

5 g kosher salt, plus more for water

2 g black pepper, freshly ground