Peel the garlic cloves. Ensure they are whole and free of blemishes.
Gently wash and pat dry the rosemary sprigs.
Combine Ingredients.
In a 1 quart saucepan, place the garlic cloves and rosemary sprigs.
Pour in enough olive oil to completely cover the garlic, about 2 cups.
Cook Slowly.
Heat the saucepan over low heat, aiming for a temperature between 200°F and 250°F. Use a thermometer to ensure the oil doesn’t get too hot. I used the lowest temp possible on my stovetop and my temperature read 220 throughout the cooking process.
Simmer gently for about about 40 minutes, stirring occasionally. The garlic should become soft, golden, and tender, but not browned.
Cool and Store.
Let the mixture cool to room temperature.
Transfer the garlic, rosemary, and oil into a clean, sterilized jar.
Seal the jar and store in the refrigerator for up to 2 weeks. Always keep the garlic submerged in oil. Make sure to label your jar so you know when you made it - eating it past the 2 week pose health risks such as botulism.