Preheat oven to 400°F. Place a large pot of salted water on to boil for the gnocchi. Chop the broccoli florets into bite-sized pieces. Destem the kale and roughly chop the leaves. Peel and mince the garlic.
Roast the broccoli
Add the chopped broccoli florets to a baking sheet and toss with 2 tsp vegetable oil and a pinch of salt and pepper. Roast until the broccoli is bright green and crisp-tender, about 5 to 7 minutes.
Cook the gnocchi
Add the gnocchi to the large pot of boiling water and cook until they float to the surface, about 3 to 4 minutes. Reserve ⅓ cup of the pasta water and drain the gnocchi. Place a large nonstick skillet over medium-high heat with the butter. Once hot, add the cooked gnocchi to the skillet and cook, tossing occasionally, until browned in places, about 4 to 6 minutes.
Finish the gnocchi
Add the chopped kale, minced garlic, and as much crushed red pepper as you like to the skillet with the gnocchi. Cook until the kale begins to wilt, about 1 to 2 minutes. Add the roasted broccoli, sun-dried tomatoes, white balsamic vinegar, reserved pasta water, and 1 tbsp olive oil to the skillet. Toss to combine and cook until the gnocchi are coated, about 1 minute.
Divide the Tuscan-style gnocchi with sun-dried tomatoes & broccoli between large shallow bowls or plates. Buon appetito!