Whisk together 1 whole egg and 1 egg yolk, brown sugar, vanilla bean paste, pumpkin puree, pumpkin pie spice, and salt until thoroughly combined. Add milk and continue mixing. Strain through a fine mesh sieve to remove any clumps.
Pour the mixture into to a microwave-safe dish. Use a spoon to remove any air bubbles. Cover with plastic wrap and prick holes in it using a toothpick.
For this next step, we are creating a water bath. Add the mixture-filled dish inside a baking dish and pour boiling water into the baking dish, up until it’s past the line of the eggs. This step is crucial to ensure even cooking to create that silky custard texture.
Microwave at 50% (500W) power level for 6-8 minutes, starting at 6 minutes. After 6 minutes, check if the center has set. If not, continue working in 1 minute intervals until the center is set when gently jiggling the dish. (Time may vary with microwaves.) Immediately remove from the water bath to prevent overcooking.
To make the brown sugar syrup: In a pan over medium-low heat, add brown sugar and water. Allow the sugar to dissolve. Reduce to a simmer until slightly thickened. Pour on top of the pumpkin flan and enjoy!