Heat 1 Teaspoon Of Olive Oil In A Small Skillet Over Medium Heat. Cook And Stir The Onions In The Oil Until Soft And Translucent, About 5 Minutes. Gently Knead Together The Softened Onions, Lamb, Egg, Bread Crumbs, Garlic, Salt, And Pepper. Divide The Mixture Into 6 Parts And Roll Into Balls, Then Cover And Refrigerate Until Ready To Use. Mix Together The Goat Cheese, Extra-Virgin Olive Oil, Basil, And Oregano Until Well Combined; Cover And Chill For 5 Minutes. Preheat An Outdoor Grill For Medium-High Heat. Working With One Portion Of Meat At A Time, Make An Indentation In The Center Of The Ball With Your Thumb. Fill The Indentation With A Heaping Tablespoon Of The Goat Cheese Mixture. Gently Pull And Form The Meat Patty Around The Cheese Filling, Making A Burger-Shaped Patty. Repeat With Each Ball Of The Lamb Mixture. Grill The Patties On The Preheated Grill Until No Longer Pink In The Center And Well Done, About 8 Minutes Per Side.