Step 1
Place a rack in lower third of oven; preheat to 400°. Combine 1½ lb. onions (about 4 small), preferably yellow, halved, thinly sliced, 3 Tbsp. unsalted butter, and ¾ tsp. Diamond Crystal or ½ tsp. Morton kosher salt in a large Dutch oven or other heavy pot over medium, cover, and cook, stirring occasionally, until onions are softened and translucent, 9–11 minutes. Uncover and continue to cook, adding splashes of water (up to ½ cup) and stirring and scraping bottom of pot often, until deep golden brown, 15–20 minutes.
Step 2
Remove pot from heat and stir 1 garlic clove, finely chopped, 2 tsp. sherry vinegar or red wine vinegar, 2 tsp. Worcestershire sauce, 1 tsp. freshly ground pepper, and 2 oz. Gruyère, coarsely grated, into onion mixture. Taste and season with more salt if needed; set aside.
Step 3
Meanwhile, if using a 14-oz. package of frozen puff pastry, cut dough in half and roll 1 half into a 10×8″ rectangle on a piece of parchment paper; reserve remaining half for another use. If using a 17.3-oz. package of frozen puff pastry, roll out 1 sheet on a piece of parchment paper just to smooth out creases.
Step 4
Lightly score a ½” border around edges of rolled out pastry (you don’t want to cut very deeply; just leave a light mark), then prick in a few spots with a fork, staying within border. Slide pastry with parchment paper onto a large baking sheet. Bake until puffed and golden, 15–18 minutes. Remove crust from oven and immediately press down on space within border with a kitchen towel to flatten slightly.
Step 5
Using an offset spatula, spread 1 Tbsp. Dijon mustard evenly over pastry, staying within border. Spoon reserved onion mixture over mustard and smooth out evenly over surface. Scatter remaining 2 oz. Gruyère, coarsely grated, on top.
Step 6
Bake tart until pastry is golden brown and cheese is melted, 10–15 minutes. Let cool 5 minutes, then cut tart into squares and top with chopped chives.