Stir oats into 3 cups water in a saucepan; bring to a boil, reduce heat to medium-low, and cook at a simmer until the oats are tender and the water is absorbed, about 20 minutes.

Stir 2 cups hot water into the cooked oats. Strain water to use as 'oat broth' into a large sauce pan. Save cooked oats for another use.

Stir pumpkin puree, sugar, herbes de Provence, salt, black pepper, and garlic powder into the oat broth with a whisk until smooth; add olive oil and stir to combine. Thin the gravy with more hot water, if desired. Place the saucepan over medium heat, bring the gravy to a simmer, and cook until hot, about 10 minutes.