Preheat your oven to 200°C (390°F). Gather your baking dish, a sharp knife, and a mandoline or vegetable peeler.
Thinly slice the potatoes into rounds about 3mm thick using the mandoline or sharp knife. Keep the slices in a bowl of water to prevent browning while you prep the other ingredients.
Trim the woody ends from the asparagus, then cut into 4-5cm pieces. If the stalks are very thick, halve them lengthwise for even cooking.
Drain the potato slices and pat them dry with a clean towel. Toss the slices with a tablespoon of olive oil, chopped thyme, salt, and pepper in a mixing bowl until evenly coated.
Layer the potato slices evenly in your baking dish, overlapping slightly to create a snug base layer. Drizzle a little more olive oil over the top if needed.
Arrange the asparagus pieces on top of the potatoes, spreading them out evenly. Sprinkle the minced garlic over the asparagus, then season lightly with salt and pepper.
Cover the dish with aluminum foil and bake in the preheated oven for 35-40 minutes. The potatoes should be tender and beginning to turn golden at the edges.
Remove the foil and increase the oven temperature to 220°C (430°F). Bake uncovered for an additional 10 minutes until the top is golden and crispy, and the aroma is inviting.
Check that the potatoes are soft when pierced with a skewer and that the asparagus is tender but still vibrant green. The top should be nicely browned and slightly crispy.
Remove the bake from the oven and let it rest for 5 minutes. This allows the layers to set, making it easier to serve clean slices.
Garnish with fresh herbs if desired, then serve warm directly from the dish, enjoying the tender potatoes and crisp-tender asparagus in every bite.