Step 1

Prepare grill for medium-high heat (or heat a large cast-iron skillet over medium-high). Cut cabbage in half through core; cut each half into 3 wedges, keeping core intact. Drizzle with 3 Tbsp. oil and rub to coat; season all over with salt.

Step 2

Grill cabbage until deeply charred on cut sides and a paring knife slides easily through center, 6–8 minutes per side. Transfer to a cutting board and let cool 5 minutes (this will allow the cabbage to soften further). Cut some wedges in half crosswise; leave the rest whole.

Step 3

Combine garlic, tahini, honey, cumin, and ¼ cup oil in a medium bowl. Finely grate zest from lemon into bowl, then cut lemon in half and squeeze juice into bowl. Add a big pinch of salt and whisk until smooth. Whisking constantly, add 3–4 Tbsp. cold water; tahini sauce should be creamy but pourable.

Step 4

Arrange cabbage wedges on a platter and spoon tahini sauce over. Scatter dill over cabbage, then sprinkle with sesame seeds. Drizzle a little oil over everything to finish.