Gluten Free Browned Butter Pear Dutch Baby

unsalted butter, divided

large eggs, room temperature

whole milk, warmed

agave syrup or honey, divided

vanilla extract

salt

all-purpose gluten free flour (I use Glutino Gluten Free Pantry All-Purpose Flour)

Bosc pears, peeled, halved, cored and sliced

ground cardamom

Powdered sugar, for dusting (for refined-sugar-free option use powdered xylitol)

scoops vanilla ice cream, for serving (optional)