In a food processor, combine garlic, basil, lemon juice, salt, walnuts, and Parmesan. Pulse until mixture is finely chopped, scraping down sides as needed. With the food processor running, slowly add olive oil. Start with ¼ cup and if pesto is too thick, add additional olive oil, 1 tablespoon at a time until desired consistency is reached. Adjust seasoning to taste.
Remove the leaves from the cauliflower, leaving stem intact. Place the cauliflower on a cutting board with the core side up. Cut the cauliflower in half, exactly down the center of the core. Make another cut about ¾ inches from the midline on each half, leaving you with two steaks and some loose florets.
Generously brush both sides of the cauliflower steaks with olive oil and sprinkle with salt. Toss loose florets with olive oil and salt as well and place them in a grill basket.
Prepare grill for medium-high heat. Place cauliflower steaks and grill basket on the grill and cook for about 8-12 minutes per side, checking occasionally. Cauliflower should be charred in spots and the core should be tender. Remove from heat.
Smother cauliflower with pesto and serve immediately.