Trim root ends and dark green tops from leeks, reserving only the white and light green parts. Slice lengthwise then thinly crosswise into 1/4-inch (6 mm) half-moons. Transfer to a large bowl of cold water and swish to release grit. Lift leeks out with a slotted spoon and drain well in a colander or on paper towels.

Sweat the leeks

In a large skillet over medium heat, melt the butter with the olive oil. Add the drained leeks and a pinch of salt. Cook gently, stirring occasionally, until very soft and translucent, about 10–12 minutes. Add the minced garlic and thyme in the last 2 minutes and cook until fragrant. Remove from heat and let cool for 5–10 minutes.

Make the Goat Cheese Filling

In a medium bowl, combine the goat cheese and cream cheese (or ricotta) and stir until smooth and spreadable. Fold in the cooled leeks, lemon zest, black pepper and the teaspoon of salt. Taste and adjust seasoning; the goat cheese may be salty already so reduce added salt if needed.

Prepare Pastry and Assemble

Preheat the oven to 200°C (400°F). Line a baking sheet with parchment paper.

If using a puff pastry sheet, unroll it on a lightly floured surface and gently roll to smooth seams. Score a 1-inch (2.5 cm) border around the edge without cutting all the way through (this helps to create a raised rim). Prick the center lightly with a fork to prevent excessive puffing.

Spread the leek-and-goat-cheese mixture evenly within the scored border, leaving the edge clear. Sprinkle grated Parmesan over the top if using.

Brush the exposed pastry border with the beaten egg (or milk) to promote browning.

Bake and Finish

Bake in the preheated oven until the pastry is puffed and golden and the filling is warmed through, about 18–22 minutes. If the edges brown too quickly, tent loosely with foil for the last 5 minutes.

Remove from oven and let rest 5 minutes. Scatter chopped parsley or chives over the tart. Slice and serve warm or at room temperature.