Activate the Yeast: Add the yeast, sugar, and warm water to the bowl of your stand mixer fitted with the dough hook attachment. Mix on low for 2 minutes to activate the yeast.
Make the Dough: Gradually add the flour and mix on medium-low (speed 2) for 3-4 minutes. Then add the salt and continue mixing for another 4-5 minutes until the dough is smooth.
Let the Dough Rise: Remove the dough from the mixer and shape it into a tight ball on a clean surface. Place the dough in a greased bowl, cover with a tea towel, and leave in a warm spot for 1 hour, or until it has doubled in size.
Prepare Whipped Feta: Add the feta, Greek yoghurt, lemon zest, a pinch of salt, and some ground black pepper to the bowl of your stand mixer with the whisk attachment. Whisk on medium speed for 2 minutes, slowly drizzling in about 2 tablespoons of olive oil. Continue whisking for another 3-4 minutes until creamy. Refrigerate until ready to serve.
Blister the Tomatoes: Heat a frying pan over high heat. In a bowl, toss the cherry tomatoes and whole chilli with a drizzle of olive oil and a pinch of salt. Once the pan is very hot, add the tomatoes and chilli. Cook for 2-3 minutes, allowing the tomatoes to blister and char slightly. Remove from the pan and let cool slightly.
Prepare the Tomatoes: Once cool, remove the chilli, chop it finely, and mix it back into the tomatoes. Lightly crush some of the tomatoes as you stir the chilli into the mixture.
Shape and Rest the Dough: Take the dough out of the bowl and place it on a greased surface. Cut it into six even pieces and shape each piece into a small ball. Cover with a tea towel and let the dough rest for 10 minutes.
Grill the Flatbread: Use your hands to flatten the dough balls into flatbread shapes. Lightly brush each with olive oil and grill over medium heat for 3-4 minutes per side, until golden and cooked through.
Serve: Serve the hot flatbread alongside the whipped feta, topped with the blistered tomatoes. Garnish with torn basil leaves and any other fresh herbs you have on hand.