Heat 3 tablespoons of the butter in an ovenproof nonstick frypan 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 teaspoon salt and several grinds of pepper.
Add the leeks, thyme, and goat’s cheese and gently stir to combine.
Wipe the frypan clean and heat the remaining 2 tablespoons butter 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.