Preheat the oven to 375°F. Line a baking sheet with parchment paper.
Get your squash base roasting. Place the cubed squash, chopped shallot, and garlic clove on the baking sheet. Drizzle with olive oil and season with salt and pepper. Give everything a quick toss to coat, spread the veg out in an even layer, and pop it in the oven. Roast the squash base until the squash is tender, about 30 minutes.
While the squash is roasting, make the mixed herb salsa verde. In a medium bowl, combine the minced shallot, lemon zest, minced garlic, capers, sherry vinegar, Dijon mustard, chili flakes, salt, pepper, chopped herbs, and olive oil. Give everything a thorough stir until evenly combined. Set aside.
Start assembling the squash patties. Set a large mixing bowl out on the counter. In the bowl of a food processor, add the pecan halves and rolled oats. Pulse this mixture until you have a coarse meal. Transfer the ground pecans and oats to the large mixing bowl.
Put the food processor bowl back on the base. Add the lentils and millet to the food processor and pulse a couple times until the lentils are slightly broken up. Add this mixture to the large mixing bowl.
Put the food processor back on the base one more time. Add the roasted squash, shallot, and garlic clove to the food processor bowl. To that, also add the ground flax, Dijon mustard, tamari, and water. Pulse this mixture a few times until you have a smooth, thick paste. You will need to pop the lid off and scrape down the sides of the bowl with a spatula at one point, just to get it all evenly mixed!
Scrape the squash purée into the large mixing bowl. To this, also add the minced thyme, nutritional yeast, onion powder, chili flakes, and a good amount of salt and pepper. Using a rubber spatula or clean hands, thoroughly mix everything together. It will feel a bit wet! Give the mixture a taste to see if the seasoning needs any adjustment.
Divide the squash patty mixture into 6 equal portions. Grab the parchment lined baking sheet that you used to roast the squash. There should be enough residual olive oil left on the paper. Spread it out evenly across the paper with your hand or a pastry brush.
Form the portions of the patty mixture into patties of approximately ¾ inch thickness. Spray the tops of the patties with oil and pop them into the oven for 35 minutes, gently flipping them over at the halfway point. The patties are done when they are golden brown and slightly firm feeling.
Serve the vegan squash patties with the mixed herb salsa verde.