In a large bowl whisk together flour, instant yeast, sugar and salt. Add warm water (about 105–115°F / 40–46°C) and 1 tablespoon olive oil. Stir with a wooden spoon until a shaggy dough forms.

Knead

Turn dough onto a lightly floured surface and knead 6–8 minutes until smooth and elastic. Alternatively use a stand mixer with dough hook on low for 4–5 minutes. Add additional flour by 1 tablespoon if dough is very sticky; dough should be soft and slightly tacky.

First rise

Lightly oil a clean bowl with remaining 1 tablespoon olive oil, place dough inside, cover with plastic wrap or a kitchen towel and let rise in a warm draft-free spot until doubled, about 1 to 1¼ hours.

Divide & rest

Punch down dough gently and divide into 2 equal portions for two medium flatbreads (or keep whole for one large). Let rest, covered, for 15 minutes to relax gluten.

Shape

On a lightly floured surface, stretch or roll each portion into a thin oval or round about 10–12 inches (roughly 1/8–1/4 inch thick). Transfer to a baking sheet lined with parchment or a lightly floured pizza peel if using a baking stone.

Prebake

Preheat oven to 500°F (260°C) with a pizza stone or baking sheet inside if available. Brush each flatbread lightly with olive oil. Bake one sheet at a time on the hot stone or baking sheet for 4–6 minutes until just beginning to blister and set but not deeply browned. Remove from oven and set aside for topping.

Lobster Topping

Prepare lobster

If using whole cooked lobster, remove meat from shells and chop into bite-size pieces (about 1/2–3/4 inch). Pat dry with paper towel to remove excess moisture.

Sauté aromatics

In a medium skillet over medium heat melt the butter. Add minced shallot and cook 1–2 minutes until softened. Add minced garlic and cook 20–30 seconds until fragrant, taking care not to brown.

Finish lobster

Add chopped lobster to the skillet and toss gently to coat in butter and aromatics, cooking 30–60 seconds just to warm through. Add lemon zest, lemon juice, heavy cream, chopped tarragon (if using), chives, salt and pepper. Cook 30–45 seconds until mixture is glossy and slightly thickened but not watery. Remove from heat and keep warm.

Assembly & Finish

Top flatbreads

Reduce oven to 475°F (245°C). Sprinkle a thin, even layer of shredded mozzarella over the pre-baked flatbreads (about half the cheese on each if making two). Spoon the warm lobster mixture evenly over the cheese, distributing pieces so each bite has lobster. Finish with a light dusting of grated Parmesan and a few flakes of red pepper if using.

Bake to finish

Return flatbreads to the oven on the hot stone or baking sheet and bake 5–7 minutes until cheese is melted, edges are golden and lobster is just heated through. Watch closely to prevent overcooking lobster.

Finish & serve

Remove flatbreads from oven. Immediately top with a generous handful of fresh arugula and a drizzle of olive oil. Squeeze lemon wedges over individual portions to taste. Slice into 6–8 pieces and serve hot.