For the crust: Combine the flour, salt and baking soda in the bowl of a stand mixer fitted with the paddle attachment. Add the butter and mix on low speed until incorporated, about 2 minutes. With the machine running, slowly add 1/3 cup water and mix until a dough forms, adding more water if needed, 1 tablespoon at a time. Transfer the dough to a lightly floured work surface and knead until smooth, about 5 minutes. Form the dough into a disc and wrap in plastic wrap. Refrigerate for 30 minutes.
Place a grill pan over medium-high heat or preheat a gas or charcoal grill. On a lightly floured work surface, roll out the dough into a 1/4-inch-thick circle, about 9-inches in diameter. Brush with olive oil. Grill for 4 minutes per side. Let cool slightly.
For the filling: In a large skillet, heat the butter and olive oil over medium-high heat. Add the mushrooms, leeks, shallot, 1 1/2 teaspoons salt and 1/2 teaspoon pepper. Cook, stirring frequently, until the vegetables are soft, about 8 minutes. Add the kale and cook until wilted, about 6 minutes. Add the broth and cranberries. Bring to a boil and scrape up the browned bits from the bottom of the pan with a wooden spoon. Season with salt and pepper.
For the cheese layer: In a food processor, combine the gorgonzola, cream cheese, sour cream, honey, lemon juice, 1/4 teaspoon salt and 1/8 teaspoon pepper. Blend until smooth.
Using a spatula, spread the cheese layer evenly over the crust. Spoon the filling on top. Cut the tart into slices and serve.
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