Preheat your oven to 375°F (190°C). Line a 12-cup muffin tin with paper liners or generously grease with olive oil or butter. Position your oven rack in the center for even heat distribution.
In a medium skillet, melt the butter or heat the olive oil over medium heat. Add the diced apples, lemon juice, honey or maple syrup, and thyme leaves. Cook for 3-5 minutes until the apples soften slightly but still maintain their shape. They should be tender but not mushy! Remove from heat and allow to cool while preparing the batter.
In a large bowl, whisk together the polenta, gluten-free flour, baking powder, salt, chopped thyme, cinnamon, and black pepper.
In a separate bowl, whisk the eggs until lightly beaten. Add the honey or maple syrup, olive oil, buttermilk, and vanilla extract. Whisk until the mixture is well combined and slightly frothy.
Pour the wet ingredients into the dry ingredients and stir gently with a wooden spoon or rubber spatula. Mix just until combined – overmixing will make your muffins tough. The batter should be thick but pourable.
Gently fold the cooled apple mixture into the batter, making sure the apples are evenly distributed. Reserve a few pieces for topping if desired.
Divide the batter evenly among the muffin cups, filling each about 3/4 full. If using, sprinkle coarse cornmeal on top of each muffin and add a few small apple pieces and a tiny sprig of fresh thyme.
Bake for 22-25 minutes, or until the tops are golden brown and a toothpick inserted into the center comes out clean or with just a few moist crumbs attached. Rotate the pan halfway through baking to ensure even browning.
Allow the muffins to cool in the pan for 5-10 minutes, then transfer to a wire rack. These muffins taste wonderful warm, at room temperature, or even lightly toasted the next day.