Start with the dough, because it will take the longest to make. In a small bowl, mix your yeast and warm water. Gently drizzle the honey over the floating yeast so it will settle at the bottom of the bowl. Let sit for about five minutes, until the yeast begins foaming.
Mix your flour, salt, activated yeast/honey mixture, and milk together in a very large bowl. Stir gently with a wooden spoon until dough starts to form, then cover your hands with flower and use them to kneed the dough. (I don't have a standing mixer, but that would work just as well if not better.)
Cover your bowl with a dry towel and set it in a warm place for a little over an hour. The dough will double in size.
You can make your pesto whenever, but I chose to do mine when my dough timer had about ten minutes left. Start by finely chopping up the basil until you have a leafy paste, then mix that in a small bowl with the olive oil. Finely chop the garlic and sunflower seeds, adjusting the size based on your preference. Mix in the grated or finely chopped cheese last. Note that the more cheese you add, the creamier your pesto will be. (A blender or food processor would work better than a chef's knife, but I don't have either of those so I had to chop everything.)
By now, your dough should be risen. Flour your countertop and gently pull the dough out of the bowl onto the flour. If it's sticky, that's fine. Work flour into the sticky parts and kneed the dough until you're satisfied with the stickiness/feel of it.
Roll your dough out into a 1/4 inch thick rectangle. Be careful not to rip it or stretch it too thin in places. (I used a soda can and my hands to roll mine out because I don't have a rolling pin, so it looks messy.)
Move your dough to a baking sheet!
Preheat your oven to 400F!
Start layering on your fillings and pesto! I'd recommend putting them in the center of your dough, not the edge like I did in the pictures. And try not to be over-ambitious by putting in more filling than you'll be able to successfully wrap your dough around.
Fold your dough around your filling so you get a tube stuffed with goodness. Be careful not to rip your dough! If you do, try to seal it back or patch it with leftover dough or pieces from other parts of the tube. (Note: I don't have a baking sheet so I used an old pizza pan and ran out of room. As a result, I had to make my "tube" into a circle. I wouldn't recommend this!! It takes longer to bake all the way through.)
Bake for ten minutes, sprinkle some cheese on top, and then bake for fifteen more minutes. (Note: I check my oven every five to make sure nothing is going wrong, but that's just me.)
Voila! Pull it out and let it cool for a bit, and then you're ready to serve! It goes great with pizza sauce or extra pesto. Enjoy!
