Position a rack in the center of the oven and heat the oven to 350°F.
Heat 2 Tbs. of the butter and 1 Tbs. of the olive oil in a 10-inch, ovenproof nonstick skillet over medium-high heat. When the butter has melted, add the leeks and a generous pinch of salt and cook, stirring, until the leeks are tender and lightly browned, about 6 minutes. Transfer to a plate, spread in an even layer, and let cool briefly.
In a large bowl, whisk the eggs with 1 tsp. salt and several grinds of pepper. Add the leeks, thyme, and goat cheese and gently stir to combine.
Wipe the skillet clean and heat the remaining 1 Tbs. each butter and olive oil over medium-low heat. When the butter has melted, add the egg mixture and gently shake the pan to evenly distribute the leeks and cheese. Cook until the eggs begin to set around the edges, about 5 minutes. Gently shake the pan to be sure the frittata isn’t sticking (if necessary, slide a spatula around the perimeter to release it). Transfer the pan to the oven and continue to cook until the frittata is set in the center, about 5 minutes. Remove from the oven and let sit for about 2 minutes. Carefully slide the frittata onto a serving plate, cut into wedges, and serve warm or at room temperature.
Serve with a simple garden lettuce salad and thinly sliced prosciutto or Serrano ham on the side.