Heat the oven to 400 F / 200 C and line a 13 x 9-inch / 33 x 23 cm sheet pan with parchment.
Unroll the puff pastry onto the pan. Using a paring knife, score a border about 2 cm / 3/4 inch from the edge without cutting all the way through, then prick the center all over with a fork.
In a mixing bowl, whisk the drained ricotta, 1 egg, 2 tbsp honey, lemon zest, and a pinch of salt until smooth.
Spread the ricotta mixture evenly inside the scored border, leaving the border itself bare.
In a separate bowl, toss the halved figs with melted butter, the remaining 2 tbsp honey, and thyme leaves. Arrange the figs cut-side up over the ricotta layer.
Brush the bare pastry border with the egg wash.
Bake for 28 to 32 minutes, until the pastry is deep golden brown and the figs are caramelized at the edges with the honey syrup bubbling.
If the figs need more color once the pastry is done, broil for 1 to 2 minutes, watching closely so the edges don't scorch.
Cool on the pan for 5 minutes, then scatter with more fresh thyme and flaky salt. Slice into 8 pieces and serve warm or at room temperature.