In saucepan over medium heat, warm strawberries until they begin to break down, about 5 minutes. Mash strawberries into a chunky purée and stir in chia seeds, honey, and lemon juice; heat for another 2 minutes. Let cool for at least 1 hour to thicken.
Spread half the peanut butter and strawberry-chia jam on 4 slices of bread, then top slices with brie cheese. Spread remaining peanut butter and jam on remaining bread slices and place on top of cheese, jam side down.
In skillet, melt butter over medium-low heat. Heat sandwiches, in batches if necessary, and adding more butter to pan if required, until bread is golden and crispy on both sides and cheese has melted, about 3 minutes per side.