To make the dough, place the yeast, honey and water in a small bowl and whisk to combine. Set aside for 5 minutes or until the mixture is bubbly. Place the flour and salt in a medium bowl and make a well in the center. Add the yeast mixture and stir together to form a dough. Turn out onto a floured surface and knead for 3-4 minutes or until smooth and elastic. The dough should be soft, but not sticky. Place in a large greased bowl, cover, and set aside in a warm spot for 15-20 minutes.
While the dough is resting, make the pesto. Add the basil, mint, parmesan, pistachios, garlic, olive oil and a pinch of salt to a food processor or blender. Pulse until until combined. Stir in the crushed red pepper flakes. Taste and adjust seasonings as needed. Set aside or store in the fridge for up to one week.
Heat a large skillet, grill pan or grill over high heat. Toss the asparagus with a little olive oil, salt and pepper. Cook until lightly charred and tender, about 5 minutes. Remove and chop into 1 inch pieces.
By this time, the dough should be ready to go. Turn the dough out and divide it into 4 equal pieces. On a floured surface, roll each piece of dough to an approximately 9 x 14 inch rectangle. Make sure your work surface is well floured, you do not want the dough to stick. Cut each rectangle in half to make 8 squares (or leave as 4 big rectangles for a larger serving).
In a small bowl, mix together the ricotta cheese, fontina cheese and lemon zest. Place 2-4 tablespoons pesto on one side of each piece of dough, leaving a 1/2 border. Add an 1/8 of the ricotta cheese mixture and then a small handful of asparagus. Fold the dough over to enclose the filling and press the edges to seal. Repeat with the remaining ingredients, you may not need to use all the pesto.
Heat a large skillet over medium heat. Brush both sides of the gozleme with oil (you may also use melted butter) and cook, in batches, for 3-4 minutes each side or until golden and cooked through. Serve with fresh basil, arugula and cherry tomatoes. Sprinkle with salt if desired.