Combine the yogurt, white wine vinegar, tarragon, salt, sugar, and Dijon mustard in a small bowl.
Whisk together the dressing until smooth. Cover with plastic wrap of lid, and place in the refrigerator until ready to serve.
Cut the radicchio head in half, making sure to go through the core. Make sure to go through the core for each time. Cut each half in 4 equal wedges to get a total of 8 wedges.
Place a grill pan on medium-high heat, so that you can some good grill marks. You can also use a BBQ to grill the wedges.
Brush both sides of the radicchio wedges with olive oil and sprinkle with sea salt.
Place carefully the wedges in the preheated grill pan or BBQ.
Cook for 2 minutes per side, just enough to get some good grill marks. Make sure to not overcook, so that they stay crisp. Remove from the grill pan and onto a clean plate.
When ready to serve, spread some of the prepared dressing on a plate. Place your desired amount of grilled radicchio over the dressing and then garnish with grated parmesan and roasted nuts.