In a medium saucepan, bring the chicken broth to a simmer. Add the arborio rice and stir. Cover, reduce heat to low, and cook for 18 to 20 minutes until the rice is tender and has absorbed the liquid, stirring occasionally.Remove from heat and stir in the parmesan cheese, butter, and salt. Spread the rice out on a baking sheet and refrigerate until completely cool, at least 1 hour.
Once the rice is cold, scoop about 2 tablespoons of rice into your hand. Press a cube of fresh mozzarella into the center, then mold the rice around it, forming a tight ball. The mozzarella should be completely enclosed. Repeat until all the rice is used, making about 18 to 20 arancini.
Set up a breading station with three shallow dishes. Place the gluten free flour in the first, beaten eggs in the second, and gluten free panko breadcrumbs mixed with italian seasoning in the third.
Roll each rice ball in the flour, then dip in the beaten egg, and coat thoroughly in the seasoned panko. Place them on a tray and refrigerate for 15 minutes to help them hold their shape.
Heat about 3 inches of oil in a deep heavy-bottomed pot to 350 degrees F. Fry the arancini in batches of 4 to 5, turning occasionally, for 3 to 4 minutes until deep golden brown and crispy all over.Use a slotted spoon to transfer them to a paper towel-lined plate.
Let them cool for about 3 minutes before serving with warm marinara sauce for dipping. The mozzarella inside should be perfectly melty and stretchy.