Take the strudel dough out of the refrigerator and let it rest at room temperature for about 10 minutes. Wash the thyme and shake dry. Pluck the leaves from the stalks, except for a few for garnishing.
Wash the pumpkin, remove seeds, cut into slices and grate coarsely. Apple wash, dry grate and quarter. Cut apple quarters into pieces and sprinkle with lemon juice. Drain sauerkraut and squeeze well.
Heat 1 tablespoon of oil in a frying pan. Sauté the sauerkraut, pumpkin and apple pieces for about 5 minutes. Add half of the goat cheese and thyme and mix well. Season to taste with salt and pepper.
Open the strudel pack. Place 1 damp tea towel on the worktop, cover with a dry cloth. Unfold 2 strudel leaves. Place 1 sheet on the cloth, 2. turn 90 °. Spread oil between the leaves.
Place the rest of the leaves on top as well. Spread a strip of breadcrumbs on the lower third of the long side. Spread pumpkin and sauerkraut mixture on top. Leave the edges (about 2 cm) free.
Spread the remaining goat's cheese in flakes over the mixture. Whisk the egg whites and brush the edges of the dough with them. Fold narrow sides inwards and roll up the strudel. Place the strudel on a baking tray lined with baking paper and brush with 1 tablespoon of olive oil.
Bake in the preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: level 3) for 20-30 minutes until golden brown. Remove and garnish with the remaining thyme.