Clean and wash the 750 g green beans. In a pot, bring salted water to a boil over high heat. Add the beans, cover, and cook for 15 minutes. Drain well.
Peel and finely dice the 2 onions and 1 garlic clove.
Heat 1 tablespoon oil in a large pan over medium-high heat. Add the 600 g minced meat and cook, breaking it apart, for 5-7 minutes until browned. Add the diced onions and garlic, cook for 1-2 minutes. Add the 1 tablespoon tomato paste and stir for 1 minute. Add the 500 g chunky tomatoes and deglaze the pan. Season with salt, pepper, paprika powder, and a pinch of sugar. Simmer uncovered for 10 minutes.
In a saucepan, heat 2 tablespoons butter over medium heat. Whisk in the 2 tablespoons flour and cook for 1 minute, stirring constantly. Gradually stir in 250 ml water, 250 ml milk, and 1 teaspoon vegetable stock. Bring to a boil, then simmer for 5 minutes. Dice the 50 g Gorgonzola and stir into the sauce until melted. Season with pepper and a pinch of salt.
Spread the cooked minced meat mixture and cooked beans in a large greased baking dish. Pour the gorgonzola sauce over it. Sprinkle the 50 g grated Gouda cheese on top.
Bake in a preheated oven (200°C/392°F for electric, 175°C/347°F for convection, or gas mark 3) for 40 minutes.