Final answer:
The type of filter that allows the most solids and coffee oils to pass into the brewed cup of coffee is a course porous medium, typically a metal filter. These filters create a full-bodied and flavorful coffee by allowing more oils and fine particles through.
Step-by-step explanation:
The type of filter that lets the most solids and coffee oils into the cup during the brewing process is a course porous medium. Filtration in coffee making is the process of removing solids from the coffee, effectively separating a heterogeneous mixture of liquid and solid. By allowing more of the coffee's oils and fine particles to pass through, a more full-bodied and flavorful cup of coffee is produced. Among the various filtration methods, such as using paper filters or metal filters, metal filters are typically less fine and thus permit more oils and fine solids to pass into the final brew. This can result in a richer flavor profile with greater body and complexity due to the presence of these compounds. Contrastingly, paper filters tend to capture more of the oils and finer solids, resulting in a cleaner, lighter cup of coffee.