Cream cake with strawberry filling

½ cup (1 stick) unsalted butter, room temperature, plus more for pan

1 ½ cups all-purpose flour (spooned and leveled), plus more for pan

2 teaspoons baking powder

½ teaspoon salt

½ cup sugar

2 large eggs plus 2 large egg yolks

½ teaspoon pure vanilla extract

½ cup whole milk

For the Filling

1 pound strawberries, hulled and thinly sliced

½ cup sugar

1 teaspoon unflavored gelatin ( from a ¼-ounce envelope)

1 ½ cups heavy cream