For the dough, in a food processor, combine both flours with the salt and pulse to mix. Add the butter and pulse until pea-size pieces form. Add the sour cream, ice water and lemon juice and pulse until the dough starts to come together. Transfer to a lightly floured work surface, gather any crumbs and knead until smooth. Pat into a disk, wrap in plastic and refrigerate until chilled, about 1 hour.
Preheat the oven to 400°F. Line a baking sheet with parchment paper.
For the filling, in a small bowl, toss the fennel with 1 tablespoon of the olive oil and season with salt and pepper. In a medium skillet, heat another tablespoon of olive oil. Add the shallot, season with salt and cook over moderately low heat, stirring, until softened and lightly browned, about 6 minutes. Remove the shallot to a small bowl and allow to cool. In the same skillet, add the fennel and cook until slightly softened and golden brown, about 3 minutes per side. Set aside.
In a small bowl, mix the ricotta with the lemon zest, garlic, 1 teaspoon thyme, 1 teaspoon minced oregano and ½ teaspoon minced rosemary. Season with salt and pepper. In a large bowl, toss the squash with the celery root and the remaining 1 tablespoon olive oil. Season with salt and pepper.
On a lightly floured work surface, roll out the dough to a 13-inch round. Transfer to the prepared baking sheet. Spread the ricotta mixture on the dough, leaving a 1-inch border. Pile the squash mixture on the ricotta, then scatter the caramelized fennel on top and top with the shallots. Fold 1 ½ inches of the dough edge over the vegetables. Sprinkle with more thyme, oregano and rosemary leaves. Brush the dough edge with the beaten egg.
Bake the crostada for 15 minutes, until it starts to brown. Sprinkle the Parmigiano over the filling and bake 15 to 20 minutes more, until the vegetables are tender and the crust is golden.
In a small bowl, mix the honey with the lemon juice and red pepper flakes (if using). Drizzle the honey mixture over the crostada just before serving.
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