Mix 125 g flour, salt, and 0.5 pack dry yeast. Add 60 ml lukewarm water and 2 tablespoons olive oil. Using a hand mixer with dough hook, form a smooth dough. Let rise in a warm place for 30 minutes.
Finely chop 2 garlic cloves and finely dice 1 onion. Heat the remaining 2 tablespoons olive oil in a pan over medium heat. Add gyros, onion, and garlic; fry for 5-6 minutes, stirring occasionally. Season with salt, white pepper, and paprika powder. Transfer to a plate and let cool for a few minutes.
Cut 100 g spring onions into rings and cut 3 tomatoes into wedges. Knead the dough again. On a floured surface, roll into a 25 x 30 cm rectangle. Cut in half lengthwise. Place the dough strips side by side on a baking sheet lined with baking paper.
Brush the dough strips with 2 tablespoons grainy mustard. Distribute the cooled gyros mixture, spring onion rings, and tomato wedges on top. Sprinkle with 75 g grated Gouda cheese. Bake in a preheated oven at 200 °C (392 °F) for 18 minutes. While baking, strip the leaves from the thyme stalk.
Remove pizza from oven. Garnish with thyme leaves and basil. Serve immediately.