For the pasta, add all ingredients into a stand mixer fitted with the paddle attachment. Beat at level 2 for 30-60 seconds until ingredients are combined. If the mixture seems to dry, add another 1/2 tsp of water. Swap out the paddle for the dough hook attachment and mix on level 2 for an additional 2 minutes. Remove dough ball and knead by hand for another 1 – 2 minutes. Cut into 4 pieces and wrap in plastic, allowing to sit on the counter for 30 minutes.
While pasta rests, preheat oven to 350F. Toss both squash in salt, pepper and olive oil. Scatter on a baking sheet and roast for 30-35 minutes until tender. Place cherry tomatoes into a roasting dish tossed in salt, pepper and olive oil and allow to roast for 35-45 minutes until juices form.
In a sauté pan, add finely diced garlic and shallots. Drizzle with a small amount of olive oil and stir occasionally over medium heat until golden. Add butter and continue to stir until soft, adding herbs as you go. Deglaze with wine, continuing to stir. Reduce down and add chicken/veg stock, allow to simmer for 10 minutes, stirring occasionally. Add chopped kale and cover on low for 2-5 minutes until wilted.
Returning to pasta, either flattening dough discs using a rolling pin or your stand mixer pasta attachment. Cut pappardelle with a wooden cutting tool or knife. Noodles should be approx. 1 inch wide. Allow to dry on a rack before boiling in heavily salted water for 3-4 minutes, until tender.
Drain into a colander and rinse with cold water, toss in olive oil and then add to your saucepan, coating noodles well. Serve warm topped with roasted squash and tomatoes.