In a food processor, combine the flour, sugar, salt, and cubed plant-based butter. Pulse until the mixture resembles coarse crumbs with pea-sized butter chunks. (If you don't have a food processor, you can work the dough with your hands in a large mixing bowl) Gradually add ice water, pulsing until the dough just comes together. Don't overwork it! Wrap the dough in plastic wrap and chill for 30 minutes to an hour.
While the dough chills, bring a large pot of salted water to a rolling boil. Blanch the trimmed green beans for 2 minutes, then immediately plunge them into an ice bath to stop cooking and preserve their bright color. Drain and set aside.
Combine all the cashew gouda ingredients in a high-powered blender and blend until smooth and creamy. Set aside. Taste and adjust seasonings as needed.
Preheat your oven to 400°F (200°C). Meanwhile, heat olive oil in a large skillet over medium heat. Add the sliced onions and cook slowly until they start to soften and turn golden brown, about 10 minutes. Lower the heat if they start to burn. Stir in the maple syrup, liquid smoke, and soy sauce, and continue cooking until the onions are deeply caramelized and jammy, about another 10 minutes.
On a lightly floured surface, roll out the chilled dough into a 10-12 inch circle. It doesn't need to be perfect – rustic is charming!
Spread the vegan gouda mixture evenly over the dough, leaving a 1-2 inch border around the edges. Top with the blanched green beans and caramelized onions, arranging them as desired.
Gently fold the edges of the dough over the filling, overlapping as needed to create a rustic galette shape. Baste the edges of the crust with plant based milk. Bake for 45 minutes, or until the crust is golden brown.