In a pot over medium heat, add olive oil. When hot, add onion. Cook for 8-10 minutes, until lightly browned. Add garlic and stir. Cook for 1-2 minutes, until garlic is fragrant.
Add oats and white wine. Stir; cook until oats have absorbed all liquid. Add pumpkin and sage; stir to incorporate.
While stirring, slowly pour in the vegetable broth. Increase heat to high; bring to a boil. Reduce heat to low and let simmer for 15 minutes, stirring frequently.
Remove pot from heat. Add nutritional yeast, thyme, salt, and pepper; stir.