Preheat the oven to 350°F. Grease a 9-inch square baking pan and line it with parchment paper if desired.
In a large bowl, beat the softened butter and sugar until pale and creamy.
Add the egg yolks one at a time, beating after each addition. Mix in the vanilla.
In a separate bowl, whisk together the flour, baking powder, and salt.
Add the dry ingredients to the butter mixture in two additions, alternating with the milk. Mix just until the batter comes together.
Spread the batter evenly into the prepared pan.
Toss the chopped rhubarb with 2 tablespoons sugar, then scatter it evenly over the cake batter.
In a clean bowl, beat the egg whites and cream of tartar until foamy.
Gradually add the sugar, 1 tablespoon at a time, beating until the meringue is glossy and holds firm peaks.
Beat in the vanilla, then spread the meringue over the rhubarb layer, reaching all the way to the edges of the pan.
Bake for 35–42 minutes, or until the meringue is lightly golden and the cake layer is set.
Cool for at least 45 minutes before slicing. Serve at room temperature for the best texture.