On one baking tray, arrange kale leaves in a single layer. Toss with two tablespoons of the olive oil, 1 teaspoon of kosher salt, and a pinch of red pepper flakes.
Make room at one corner of the tray for 4 slices of lemon, brushed with olive oil on both sides and sprinkled with kosher salt.
Rinse off the baby eggplants. Place on a second baking tray and toss with olive oil. Place both trays in the oven.
Remove baking sheet with kale and lemons after about 15 minutes. Kale leaves should be slightly crispy and lemons should have a little char.
Remove tray with eggplants after about 45 minutes, turing them partway through. Eggplants may burst during roasting, which is fine - let them keep going.
Once kale, lemons, and eggplant are all out of oven, turn the temp down to 350.
While eggplants cool, cut the pitas into eighths. Arrange on a baking tray and brush with olive oil. Sprinkle with za'atar and sea salt, and bake in oven for 10-12 minutes.
Place roasted kale, parsley, lemon slices, garlic cloves, tahini, remaining 1 1/2 teaspoons of salt, smoked paprika, and lemon juice into the bowl of a food processor. Remove skin and stems from eggplants and add pulp to bowl as well.
Pulse briefly, then add remaining two tablespoons of olive oil. Pulse again until ingredients are incorporated. The result should rather textured, but keep pulsing if you prefer smoother baba ghanoush.
Transfer baba ghanoush to a small serving bowl. Top with chopped parsley, a pinch of smoked paprika, and a drizzle of olive oil. Serve with warm toasted pitas.