Heat oven to 400 degrees. In a small bowl, mix strawberries with 1 tablespoon of granulated sugar and transfer to a parchment-lined baking sheet. Roast until the strawberries have released a bit of juice and are just tender, 10 to 15 minutes. Set aside to cool.
In a small saucepan, melt butter, letting it cook until it turns nut brown and smells toasted, about 5 minutes. Pour into a heatproof bowl and let cool. (Do not scrape up any black bits from the bottom of the pot.)
Meanwhile, in a large bowl, combine sugar, almond flour, all-purpose flour and salt. Using an electric mixer fitted with the whisk attachment and set on low speed (or use a whisk and a strong arm), beat in egg whites until the flour mixture is damp. Add butter and beat on medium-high speed (or vigorously by hand) until very smooth, about 2 minutes. Beat in vanilla. At this point, the batter can be used immediately or refrigerated for up to 4 days without the strawberries.
Right before baking, drain the roasted strawberries from their liquid and blot on a paper towel or clean cloth. Fold the roasted strawberries into the batter. (You may have about 1 to 2 tablespoons of strawberry syrup left to add to yogurt or seltzer.)
Butter 12 (½-cup) muffin cups and coat all over with a little granulated sugar. Divide batter across the cups, and bake until financiers are golden brown and the tops spring back when lightly pressed, 15 to 25 minutes. Cool on a wire rack before unmolding.