Combine warm water, yeast, and 1 teaspoon sugar in a small bowl. Let stand until yeast softens and forms a creamy foam, about 5 minutes.

Measure flour into a mixing bowl. Combine warm milk, 2 teaspoons sugar, and salt in a separate bowl; mix milk mixture, yeast mixture, and oil into flour to form a dough. Knead until smooth. Cover and let rise until tripled in volume, about 3 hours.

Deflate, cover, and let rise again until doubled in size, about 3 hours.

Deflate dough again and chill for 20 minutes.

Massage butter until pliable but not soft and oily. Pat dough into a 14x8-inch rectangle. Smear butter over top two-thirds, leaving a 1/4-inch margin, and fold in thirds.

Turn 90 degrees, roll into a 14x6-inch rectangle, fold in three, sprinkle with flour, and chill wrapped dough for 2 hours.

Repeat rolling and folding process a second time and chill for another 2 hours.

Preheat oven to 475 degrees F (245 degrees C).

Shape croissants by rolling out dough to 20x5-inch rectangle, dividing in halves, cutting triangles, elongating each triangle, and rolling up.

Arrange croissants on baking sheets, glaze with egg wash, and let rise until puffy.