Peel the potatoes and dice them coarsely, pour in water to cover them, pour in 2-3 tbsp oil and put on the stove to boil for 15 min.
Once they're boiled, take them out with slotted spoon, add the halved mushrooms to the same water and leave them to boil for 10 min. Take the mushrooms out of the water and put them in another container. For now, don't throw out the water.
Put another pot with clean water on the stove with a little salt and once it comes to a boil, add the broccoli, torn into rosettes, and blanch them for 3-4 min. Take them out with a slotted spoon and drop them in a container with icy-cold water.
This way they'll retain their green color. Cut the carrot into slices, put them in the same water and boil for another 3-4 min., then take them out into a bowl.
Mix together all the vegetables, sprinkle them with 3-4 tbsp oil and pour on a little of the broth in which you boiled the potatoes. Sprinkle with pressed garlic, a little black pepper and dill and transfer to a medium-sized oven dish.
Preheat the oven to 536°F (280 °C) on the grill function, with the fan on. Put the veggies in it to bake a bit for 15 min.