
This easy puff pastry tart is topped with fresh green beans, sliced mixed mushrooms, plenty of melty cheese, and crispy shallots.
Preheat oven to 425°. Line a work surface with a large piece of parchment.
Bring a large pot of salted water to a boil and cook green beans 2 minutes. Using a spider or slotted spoon, transfer beans to a bowl of ice water to shock and stop cooking. Drain green beans on paper towels.
In a large skillet over medium-high heat, melt butter until foam subsides. Cook mushrooms, stirring occasionally, until starting to lightly brown, about 5 minutes. Add garlic and thyme and cook, stirring, until fragrant, about 1 minute more; season with 1/2 teaspoon salt. Transfer mushroom mixture to a plate.
In a medium bowl, combine ricotta, goat cheese, and 1/4 teaspoon salt until smooth. In a small bowl, whisk egg and 1 tablespoon water.
Arrange puff pastry on prepared parchment. Using a rolling pin, roll to a 12"-by-10" rectangle. Cut rectangle in half to make 2 (10"-by-6") rectangles. Brush both sheets with egg wash. Transfer pastry to a parchment-lined baking sheet.
Spread ricotta mixture onto puff pastry, leaving a 1/2" border. Top with a single layer of green beans, mushroom mixture, and cheddar.
Bake tarts until edges are golden brown and cheese is browning in some spots, about 25 minutes. Sprinkle tarts with a pinch of salt.
Meanwhile, in a small saucepan over medium heat, cook shallots and oil, stirring occasionally, until oil begins to bubble around shallots, 2 to 3 minutes. Reduce heat to medium-low and continue to cook, stirring occasionally, until shallots are golden brown and crisp, 4 to 5 minutes more. Using slotted spoon, transfer shallots to a paper towel-lined plate; season with a pinch of salt. Let cool slightly.
Top tarts with crispy shallots, slice, and serve.