If your frozen spinach is still frozen, thaw it and squeeze out as much excess water as possible; set the 3/4 cup spinach aside.
In a medium bowl, combine the squeezed spinach, 1 cup chopped marinated artichokes, 1 cup shredded gouda or fontina, 1/2 cup shredded mozzarella, 1/4 cup grated parmesan, 1 grated garlic clove, 1/4 cup chopped fresh basil, and a pinch of red pepper flakes. Mix until evenly distributed.
Prepare the pitas: cut open one side of each pita to create a pocket. If a pita has no pocket or you prefer, slice that pita in half so you have two open rounds to fill.
Divide the cheese-and-vegetable mixture into four equal portions and stuff each pita pocket (or each open pita half) with one portion, pressing gently so the filling is compact but not overflowing.
Spread the 3 tablespoons salted butter evenly over the outside surfaces of each filled pita (both sides). Use softened or slightly melted butter if needed to make spreading easier.
Heat a large skillet over medium heat. Working in batches so the pan isn’t overcrowded (1–2 pitas at a time, depending on pan size), place the buttered pitas in the skillet and cook until golden and the cheese is melted, about 3–4 minutes per side, pressing lightly with a spatula as they cook.
Transfer cooked pitas to a cutting board, let rest briefly, then slice if desired. Serve drizzled with honey and with extra red pepper flakes for sprinkling, if you like.