Preheat the oven to 400°F. Peel the beets. Wrap the red beets in one sheet of tinfoil and wrap the orange beets in another. Roast for 60-75 minutes or until soft. Let them cool.
Make the beet purée for the crust. Take 1/2 cup of the cooked red beets from above and add it to a blender with 1/4 cup water. Blend until thick and smooth, and put 1/3 cup of the purée into the fridge to cool and use in the crust.
To make the crust, cube the butter into small pieces. Add the butter to a bowl with the flour and salt. Working quickly, use your hands to smash and press the butter into flat pieces, tossing in the flour and mixing to create a sandy, shaggy dough. It won't come together, but as soon as you can smash together chunks and they'll hold for a few moments before crumbling, you are ready to add the beet purée.
Add the beet purée into the bowl and mix with your hands. You'll see the dough become sticky and start to form together, we love that! You can either work the dough until it is fully pink, or leave the beet coloring speckled throughout. I prefer the latter, but either works. Move the dough to a cool surface, press it down until it is about 1" high, wrap it with plastic wrap and use a rolling pin to roll it out into a smooth rectangle. Let this chill for 30 minutes or more while you prep the rest of the recipe.
To make the salsa verde layer of the tart, mix together the chopped parsley, minced shallot, sliced garlic, preserved lemon and red pepper flakes to a bowl. Drizzle in the vinegar and olive oil and mix. Season with salt to taste. This should be a relatively dry, choppy sauce. Set aside.
Thinly slice all your beets. Set 1/3 of the golden beet slices aside, and lay red beet slices on top of them to "dye" them pink.
When the tart dough is fully chilled, lay it out on a floured surface. Preheat the oven to 375°F.
Slice from one corner of dough rectangle and end in the center, this will be the indent of the heart shape. Begin to gently roll out the dough until it is about 1/2 cm thick.
Evenly spread on the salsa verde, then layer the beets on top. I like to start with the red beets at the bottom, then the dyed pink beets, then the golden beets.
Fold the tart crust over the edges. Brush the tart crust with the beaten egg. If you can chill the dough for another few minutes while the oven preheats, that's great, but it can also go right into the oven.
Bake for 35-45 minutes. Remove from the oven and drizzle a bit of oil and vinegar on top of the beets to create some extra shine. Grate on some ricotta salata, and serve warm!