Remove the pizza dough from the fridge, place it in a lightly oiled bowl, and let it rest at room temperature to make it easier to stretch and work with.
Meanwhile, preheat your grill to medium-high. When preheated, cook the bacon slices on the grill until crisp. Remove from the grill and cut into large pieces and set aside.
In a small mixing bowl, combing 1 1/2 tablespoons of olive oil with the garlic and Italian seasoning then toss in the spinach. Season with salt and pepper and set aside.
Stretch out the dough into a large round that is approximately 30 t0 35 centimeters across. Brush the top of the dough with some of the remaining oil and gently lift the dough onto the grill, oil-side down. Close the lid and cook for two to four minutes. Check the underside of the crust and if it is not browning, leave it for another minute or so until golden.
When the bottom of the crust is golden and grilled, brush the top of the dough with the remaining oil and carefully flip the pizza crust using a pair of tongs. Top the pizza with the spinach and garlic mixture followed by the cheese and cherry tomatoes, and bacon, making sure to leave little gaps for the eggs. Crack the eggs onto the pizza, sprinkle the whole pizza with sesame seeds, then season with salt and pepper. Close the lid of the grill and cook for five to eight minutes until the underside of the crust is golden and the eggs are set and cooked to your liking.
Remove the pizza from the heat onto a wooden cutting board, allow it to cool slightly, top with some basil, if using, then cut into ten to 12 slices and serve.