6 tablespoons unsalted butter, softened, plus more for greasing
Vegetable oil, for frying
1 cup granulated sugar
1 teaspoon kosher salt
1 teaspoon freshly ground black pepper
Directions
Make the jam: Preheat the broiler to high and line a sheet pan with foil. Add the strawberries to the pan and toss with the sugar, salt and pepper. Broil until lightly charred, 3 to 4 minutes.
Transfer the contents of the pan to a medium saucepan and bring to a simmer over medium heat. Cook, stirring often, until thickened, 20 minutes. Transfer to a blender with the lemon juice and vanilla. Purée until smooth, then transfer to a bowl and let cool completely.
Make the dough: In the bowl of a stand mixer fitted with a dough hook attachment, mix together the milk, sugar and yeast. Let sit until the mixture is foamy, 15 minutes. Add the flour, salt, eggs and butter, and mix on medium speed until a smooth dough forms. Transfer the dough to a large greased bowl, cover with plastic wrap and proof for 1 hour.
After the first proof, the dough should have doubled in size. Punch it down in the bowl, cover with plastic wrap and allow to proof again for 45 minutes.
While the dough proofs for a second time, make the salt-and-pepper sugar: In a medium bowl, stir together the sugar ingredients, then set aside.
Make the doughnuts: Heat 2 inches of vegetable oil in a 6-quart Dutch oven to 350º. On a lightly floured surface, roll out the dough to a ½-inch thickness. Using a 3½-inch ring cutter, punch out doughnuts. Reroll the scraps as needed to get 12 doughnuts.
Line a baking sheet with a wire rack. Working in batches, fry the doughnuts, flipping once, until golden brown and puffed, 1 to 2 minutes per side. Transfer the cooked doughnuts to the prepared baking sheet to drain.
As soon as you can handle the fried doughnuts, toss each one in the salt-and-pepper sugar to coat completely. Let cool for 5 minutes.
Using a squeeze bottle, fill each doughnut with the strawberry jam and serve.