Poach the artichokes: Trim outer leaves and tops; keep in lemon water. Dry and submerge in olive oil with garlic, marjoram, and thyme. Cover tightly and poach at 300°F for about 45 minutes, until tender. Cool in the oil.
Tuna filling: Blend/fluff tuna, then fold in Parmigiano and chopped parsley. Season lightly and chill.
Roasted tomatoes: Halve Roma tomatoes; season with salt, pepper, a pinch of thyme/marjoram, and a drizzle of the perfumed poaching oil. Roast at 325°F for 20–30 minutes. Cool.
Assembly: Scoop artichoke centers; pipe or spoon in tuna mixture. Set each atop a roasted tomato half, drizzle with a little poaching oil, and finish with parsley.