Bring a large pot of salted water to a boil over high heat. Line a baking sheet with a wire rack.
Combine the mayonnaise, lemon zest, lemon juice, a pinch of salt and a couple grinds of pepper in a small bowl. Whisk until smooth.
Cut two 1 1/2-inch-thick steaks out of the center of the broccoli. Reserve the extra broccoli for another use.
Add the broccoli steaks to the boiling water and cook until bright green and crisp-tender, 1 to 2 minutes. Transfer to the prepared baking sheet. Blot both sides with paper towels to remove any excess water. Combine the garam masala and sumac in a small bowl, and then season the broccoli liberally all over with the spices, salt and pepper.
Heat a large cast-iron pan between medium and medium-high heat. When the pan is hot, add 2 tablespoons of the oil and swirl to coat, adding more oil as needed to fully coat the pan. Add the broccoli steaks and cook until deeply browned on the first side, 2 to 3 minutes. Carefully flip and cook until deeply browned on the second side and the broccoli is just tender, 2 to 3 minutes. Transfer the broccoli steaks back to the prepared baking sheet.
Combine the celery leaves, walnuts, apples, parsley, pepitas, chopped celery, vinegar, the remaining 2 tablespoons oil, a large pinch of salt and a couple grinds of pepper in the bowl of a miniature food processor. Pulse until finely chopped, adding oil as needed to thin out the pesto to the desired consistency. Season with additional salt and pepper if needed.
To serve, spread the aioli on the bottom of 2 serving plates. Add 1 broccoli steak to each plate, top with a couple spoonfuls of the pesto and garnish with the sliced chile. Drizzle with oil to finish.