Step 1. Place a rack in middle of oven and preheat to 400°. If using a 17.3-oz. package frozen puff pastry, thawed, place 1 sheet on a piece of parchment paper; brush off excess flour. Lightly brush surface with water. Stack second sheet on top and roll out together into a 16×12″ rectangle.. Step 2. If using a 14-oz. package frozen puff pastry, thawed, place sheet on a piece of parchment paper; brush off excess flour. Roll into a ⅛”-thick rectangle, smoothing any creases as needed.. Step 3. Using a paring knife, lightly score dough 1″ in from edges to form a border. Prick pastry all over with a fork, staying inside border. Transfer on parchment to a baking sheet; chill.. Step 4. Combine 3 garlic cloves, finely grated, 8 oz. cream cheese, room temperature, 2 oz. Pecorino Romano or Parmesan, finely grated (about 1 cup), and ½ tsp. freshly ground pepper in a small bowl. Using a rubber spatula, smash and stir until smooth. Mix in 1 large egg, beaten to blend. Toss one 12–14-oz. jar oil-marinated quartered artichoke hearts, drained, and 8 oz. asparagus, ends trimmed, halved lengthwise if thick, cut into 2″ pieces, in a medium bowl to coat asparagus in marinade.. Step 5. Spread cream cheese mixture over pastry, staying inside border. Arrange artichokes and asparagus over (some filling will be exposed). Brush some of remaining 1 large egg, beaten to blend, over exposed pastry, then fold edges at score marks up and over filling, pressing gently at corners to adhere. Brush exposed pastry with more beaten eggs (you may not use all of it) and bake galette until edges are puffed and deep golden brown, 40–45 minutes. Let cool 10 minutes.. Step 6. Toss 3 oz. baby arugula (about 3 cups), 2 Tbsp. extra-virgin olive oil, 2 Tbsp. red wine vinegar, and a pinch of flaky sea salt in a large bowl to coat; season salad with pepper. Mound salad on top of galette just before serving.
