Preheat your oven to 400 degrees F and line a large baking sheet with foil or a silicone baking mat. Add the tomatoes to the pan, drizzle with olive oil and season with a generous amount of salt and pepper. Place in the oven and roast for 8-10 minutes or until you begin to see the tomatoes start to blister. Remove from oven and set aside.
In a large skillet, add the 1 1/2 sticks of unsalted butter over medium heat. Taking a spoon, swirl the butter until it has melted. Continue to "swirl" the butter for 5-6 minutes until it just begins to brown (it's ok if the butter is bubbly), then remove from heat. The butter can quickly go from brown to burnt, so as soon as it begins to brown and a nutty aroma fills the air, remove the pan from the heat immediately. Set aside.
Bring a large pot of salted water to a rolling boil. Add the pasta and cook until al dente, about 8-10 minutes. Drain and set aside.
While your pasta is cooking, prepare your veggies. In a large saute pan, melt the remaining 2 tablespoons of butter over medium heat. Add the mushrooms, and cook for 5 minutes. Then add your asparagus, broccoli and garlic. Season with salt and pepper and saute until the veggies are bright and begin to soften, about 5 more minutes. Add the kale and cook for 1-2 minutes or just until the kale has wilted. Remove from heat.
In a large bowl, toss together the blistered tomatoes, brown butter, pasta, and sautéed veggies. Serve the pasta with a fried of poached egg on top and sprinkle with sliced green onions and parmesan cheese.