How to Make It
Preheat the oven to 350°. In a small bowl, coat the beet with 1 teaspoon of the olive oil and sprinkle with a generous pinch of salt. Wrap the beet in foil and roast in a pie plate until tender, 1 hour. Let cool, then peel the beet and slice it 1/4 inch thick. Transfer to a heatproof bowl and add the onion.
In a medium saucepan, combine the white vinegar, rice vinegar, sugar and 2 1/2 tablespoons of salt. Bring to a boil over moderate heat, stirring to dissolve the sugar. Pour the brine over the beet and onion and let cool, about 1 hour.
Light a grill or preheat a grill pan. Coat the pineapple slices with the remaining 1 teaspoon of olive oil and a pinch each of salt and crushed red pepper. Grill the pineapple until warm and lightly charred, 2 minutes per side. Transfer to a plate and keep warm.
In a large nonstick skillet, melt the butter. Add the eggs and cook over moderate heat until the whites are set and the yolks are slightly runny, about 3 minutes. Remove from the heat and season with salt.
Layer the pickled beets and onions on April’s Essential Burgers. Top with the grilled pineapple rings and the fried eggs and serve.