Butter is the fat of choice for most baking; it has great flavor and can be used at different temperatures to produce very different textures in the final product. We use unsalted butter for most of our baking needs; this allows us to control the seasoning of the final product, as sodium levels vary between different salted butter products. To soften butter, cut into 1-tablespoon pieces and let stand on a plate for 20 minutes; with more surface area exposed to the area, it'll warm faster. Softened butter should be between 65 and 67 degrees F. If a recipe calls for butter that's been melted and cooled, it should register 85 to 90 degrees F.
Coconut oil is sold in two forms, both solid at room temperature: refined, which has virtually no taste or aroma, and virgin, which retains a strong coconut flavor. Since we have limited use for an oil that makes food smell and taste like a piña colada, we tend to use refined coconut oil in most recipes. We use melted and cooled coconut oil in our Vegan Chocolate Chip Cookies; it performs just as well as melted butter (without the sweet dairy flavor, of course).
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