Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper.
Roll out the thawed puff pastry into a 12-inch circle on a floured surface and transfer it to the prepared baking sheet.
In a mixing bowl, combine ricotta, 2 tablespoons honey, and vanilla extract; spread this mixture evenly over the pastry, leaving a 2-inch border.
Toss sliced strawberries with cornstarch and sugar, then arrange them over the ricotta layer.
Fold the pastry edges over the filling, pleating as you go, then brush the edges with the beaten egg.
Bake the galette for 25 to 30 minutes until the pastry is golden brown, then let it cool slightly.
To make balsamic pearls, heat balsamic vinegar and agar-agar powder in a small saucepan, stirring until dissolved; simmer for 1 minute, then cool slightly.
Using a dropper, drip the balsamic mixture into chilled vegetable oil to form small pearls; strain and rinse the pearls with water.
Drizzle the galette with honey, top with the balsamic pearls and fresh mint leaves, and serve warm or at room temperature.