Make the Dough: In a stand mixer bowl, whisk flour, sugar, yeast, and salt. In a jug, whisk lukewarm milk, melted butter, and egg. With mixer on low with dough hook, combine wet and dry. Knead on medium 8-10 min until smooth & elastic. Form into a ball, place in oiled bowl, cover, and let rise until doubled (1-1.5 hrs) or refrigerate overnight.

Caramelize Onions: While dough rises, melt 3 tbsp butter with oil in a large skillet over medium heat. Add sliced onions, cook 10 min. Reduce heat to medium-low, stir in brown sugar, ½ tsp salt, and pepper. Cook 45-60 min, stirring occasionally, until deep golden brown. Add sherry (if using) and thyme, cook until liquid evaporates. Cool completely.

First Laminate: Punch down risen dough. On floured surface, roll to a 10x15" rectangle. Grate cold butter over dough, leaving a 1" border. Fold in thirds like a letter. Rotate 90°, wrap in plastic, chill 30 min.

Second Laminate & Fill: Roll chilled dough to a 10x15" rectangle. Spread cooled onions evenly, drizzle with Dijon, and sprinkle with 1 cup Gruyère. Fold in thirds again. Wrap and chill 30 min.

Shape & Final Proof: Roll dough to a 12x18" rectangle. Cut into 6 long strips, then cut each strip into 6 squares (36 total). Butter a 9x13" dish. Place squares in dish haphazardly, stacking for a pull-apart effect. Cover, let rise 45-60 min until puffy.

Bake: Preheat oven to 375°F (190°C). Brush rolls with egg wash, top with remaining ½ cup cheese and flaky salt. Bake 25-30 min until deep golden brown. Tent with foil if browning too fast. Cool in pan 15-20 min before serving warm.