An important goal of online platforms is to enable content discovery, i.e. allow users to find a catalog entity they were not familiar with. A pre-requisite to discover an entity, e.g. a book, with a search engine is that the entity is retrievable, i.e. there are queries for which the system will surface such entity in the top results. However, machine-learned search engines have a high retrievability bias, where the majority of the queries return the same entities. This happens partly due to the predominance of narrow intent queries, where users create queries using the title of an already known entity, e.g. in book search "harry potter". The amount of broad queries where users want to discover new entities, e.g. in music search "chill lyrical electronica with an atmospheric feeling to it", and have a higher tolerance to what they might find, is small in comparison. We focus here on two factors that have a negative impact on the retrievability of the entities (I) the training data used for dense retrieval models and (II) the distribution of narrow and broad intent queries issued in the system. We propose CtrlQGen, a method that generates queries for a chosen underlying intentnarrow or broad. We can use CtrlQGen to improve factor (I) by generating training data for dense retrieval models comprised of diverse synthetic queries. CtrlQGen can also be used to deal with factor (II) by suggesting queries with broader intents to users. Our results on datasets from the domains of music, podcasts, and books reveal that we can significantly decrease the retrievability bias of a dense retrieval model when using CtrlQGen. First, by using the generated queries as training data for dense models we make 9% of the entities retrievable-go from zero to non-zero retrievability. Second, by suggesting broader queries to users, we can make 12% of the entities retrievable in the best case.