Remove the burrata and pumpkin butter from the refrigerator and allow to come to room temperature while you prepare the toasts. Combine the burrata and salt in a small bowl and mash with a fork until smooth.
Heat the butter over medium-low heat in a skillet until it bubbles. Keep swirling the butter in the pan until it starts to darken in color. Add the sage leaves and saute until crispy. Remove onto paper towels too cool.
Preheat oven to 450 degrees. Slice the loaf of bread into thick slices and arrange on a baking sheet. Brush with olive oil on the sides that face up. Toast the bread for 12 minutes.
While the bread is toasting, make the fig syrup: Combine fig preserves and 1 Tbsp. of water in a small saucepan. Heat over low heat until the mixture thins out and becomes syrupy.
Remove the toasts from the oven. Spread a layer of pumpkin butter, then the burrata. Drizzle with fig syrup and top with crispy sage leaves.