Remove the thick inner stem from the cauliflower, slice into thick 1-inch slabs. Preheat a grill pan over high heat. Rub the cauliflower with olive oil and arrange the pieces in a single layer and flip every few seconds for 4-5 minutes until charred and tender. Transfer the cauliflower to a mixing bowl.
Peel and dice the potato in half and transfer to a sauce-pan. Cover with boiling water and cook for 6-8 minutes. Stir in the peas and cook for a further two minutes. Add these vegetables to the cauliflower.
In a food processor, pulse together the pesto ingredients plus two tablespoons of water until smooth. Spoon the mixture onto the vegetables, add the nuts, and mix thoroughly. Cover and chill for 10 minutes to blend the flavors.
Garnish each serving with a few nuts and/or vegan parmesan if using.