Heat olive oil in a medium skillet over medium heat until shimmering. Add onions and cook until softened and just translucent, 8 to 10 minutes, stirring occasionally.
Add in wine, sugar, thyme, vinegar, and salt. Bring to a boil, then reduce heat low, and let simmer until liquid thickens and becomes syrupy, about 1 hour, stirring occasionally.
Season with additional salt and pepper to taste. Transfer onion jam to a bowl and let cool, then serve or store in an airtight container in the refrigerator for up to 2 weeks, letting onion jam return to room temperature before using.
