Mash the boiled potatoes and mix with minced garlic. Stir in the beaten egg and season with basil, oregano, salt, and pepper. Gradually add flour until the mixture becomes tough to stir.
Transfer the dough to a floured board and knead until it no longer sticks to your hands.
Roll the dough into a log approximately 1-2 cm thick, cutting it into segments every 2-3 cm. Optionally, press with a fork or thumb to make indentations.
Boil in lightly salted water until they float to the surface, then cook for a few more minutes. Remove from water.
In a skillet, melt a tablespoon of butter over medium-low heat until it begins to brown. Add the gnocchi, increase the heat to medium, and cook until golden brown on both sides. Repeat with remaining gnocchi and butter.