For the sauce, finely dice the shallot and garlic. Pluck the thyme leaves from the stems and chop. Heat 1 tbsp. oil, sauté shallot, garlic and thyme until translucent. Deglaze with vegetable stock, boil to half and cool for 10 min.
Pour the stock into a tall mixing bowl. Add half of the capers, juice of one lemon and egg yolk and blend finely with a hand blender. Add the rest of the oil in a thin stream and whisk it all together to make a creamy mayo. At the end, drain the tuna, add to the mayo form and mash very finely. Season with salt, pepper and 1 pinch of sugar.
Remove the peel from the white asparagus spears, cut only the lower third of the green asparagus spears, and cut the ends of the asparagus spears into small pieces. Cut asparagus spears diagonally in the middle. Tie the veal medallions into shape with spagat. Carefully score quail eggs with a sharp kitchen knife, then beat and shape individually into 4 cups.
Cover white asparagus spears with cold water in a saucepan, season with 1 pinch of sugar and salt, and bring to a boil. Remove the saucepan from the stove and let the asparagus stand for 15 minutes. Bubble green asparagus with sugar and salt for 3-4 min. Drain both types of asparagus and keep warm.
At the same time, brush a grill pan with 1 tbsp oil. Season veal medallions with salt, season with pepper and grill over medium heat for 4 min on each side.
Heat remaining oil in a b