Preheat the oven to 440°F.
Season the salmon: Arrange the salmon steaks on a large plate. Sprinkle with black pepper, ½ tsp paprika, and ¼ tsp salt. Rub the spices onto the salmon evenly. Set aside.
Season the vegetables: Line a baking sheet with parchment paper. Combine green beans, potatoes, and baby carrots on the sheet. Season with 1 tbsp olive oil, ½ tsp paprika, and garlic powder. Mix well to coat the spices evenly.
Cook the vegetables: Remove the green beans from the baking sheet and put them in a bowl. Transfer the baking sheet to the oven and bake the potatoes and carrots for 10 minutes. After that, place the green beans onto the tray along with the other vegetables and bake for another 10 minutes. Once the timer rings, take the tray out of the oven and set aside.
Make the sauce: Heat a small saucepan over medium heat. Add white wine and let it boil for 15 seconds. Add unsalted butter and whisk vigorously until fully melted. Add heavy cream and whisk it into the sauce. Continue to add whole milk, grated Parmesan cheese, and the remaining ¼ tsp salt. Whisk well until emulsified. Turn off the heat and set aside.
Coat the salmon: Add all-purpose flour to a plate. Use a tong to pick up the salmon and dip it into the flour. Coat the fish evenly with flour on both sides. Once coated, transfer to another plate and set aside.
Sear the salmon: Heat a grill pan over medium heat. Add the remaining ½ tbsp olive oil to the pan. Once it’s hot, add the salmon and sear for about 2 minutes or until just cooked. Flip and cook for another minute or until golden brown on both sides. Add garlic and thyme. Cook for 30 seconds or until fragrant. Turn off the heat. (If your grill pan is small, you can cook 1 or 2 pieces at a time like we do in the video.)
Serve: Arrange a stack of vegetables in the center of a serving plate. Place a salmon steak on top. Pour a spoonful of the sauce over the salmon. Sprinkle with freshly chopped parsley and serve.