Combine potatoes, onion, and summer savory in a pressure cooker with water to cover. Close cooker securely and place pressure regulator over vent according to manufacturer's instructions. Adjust heat until regulator is gently rocking. Cook at high pressure until potatoes are tender, about 5 minutes. Let pressure release naturally according to manufacturer's instructions; unlock and remove lid.
Stir butter, bread, salt, and pepper into the potato mixture. Transfer stuffing to an oven-proof glass dish. Cover with plastic wrap and refrigerate for 15 to 20 minutes.
Preheat the oven to 350 degrees F (175 degrees C).
Mix eggs into the stuffing.
Bake in the preheated oven until set, 30 to 40 minutes.