Add olive oil, garlic, and red onion to a large saucepan set over medium heat. Season with salt and black pepper, to taste, and stir to combine.
Add the rosemary, cinnamon, and crushed red pepper flakes to the pan. Cook, stirring occasionally until the onion softens and the spices become very fragrant approximately 4-5 minutes.
Add the lemon juice, peaches, honey, and water to the skillet and stir to combine. Increase the heat to medium-high and bring to a rapid boil. Immediately reduce heat to medium and simmer, stirring occasionally, until the peaches are soft and the mixture starts to thicken approximately 10-12 minutes.
Remove from heat and cool for several minutes. Working in batches if necessary, transfer the warm peach mixture to a blender and quickly pulse for a few seconds just until blended, but not completely smooth.
Use immediately or store in the refrigerator in an airtight container for up to 3 to 4 days. Enjoy!