I've tried the solutions above, some of them don't work in combination with auditing, and none seems to set correctly the MongoCustomConversions
A solution that works for me is the following
@Configuration
public class MongoConfig {
    @Bean
    public MappingMongoConverter mappingMongoConverterWithCustomTypeMapper(
            MongoDatabaseFactory factory,
            MongoMappingContext context,
            MongoCustomConversions conversions) {
        DbRefResolver dbRefResolver = new DefaultDbRefResolver(factory);
        MappingMongoConverter mappingConverter = new MappingMongoConverter(dbRefResolver, context);
        mappingConverter.setCustomConversions(conversions);
        /**
         * replicate the way that Spring
         * instantiates a {@link DefaultMongoTypeMapper}
         * in {@link MappingMongoConverter#MappingMongoConverter(DbRefResolver, MappingContext)}
         */
        CustomMongoTypeMapper customTypeMapper = new CustomMongoTypeMapper(
                context,
                mappingConverter::getWriteTarget);
        mappingConverter.setTypeMapper(customTypeMapper);
        return mappingConverter;
    }
}
public class CustomMongoTypeMapper extends DefaultMongoTypeMapper {
    public CustomMongoTypeMapper(
            MappingContext<? extends PersistentEntity<?, ?>, ?> mappingContext,
            UnaryOperator<Class<?>> writeTarget) {
        super(DefaultMongoTypeMapper.DEFAULT_TYPE_KEY, mappingContext, writeTarget);
    } 
    @Override
    public TypeInformation<?> readType(Bson source) {
    /**
     * do your conversion here, and eventually return
     */
    return super.readType(source);
    }
}
As an alternative, you could use a BeanPostProcessor to detect the creation of a mappingMongoConverter, and  add your converter there.
Something like
public class MappingMongoConverterHook implements BeanPostProcessor {
    @Override
    public Object postProcessAfterInitialization(Object bean, String beanName) throws BeansException {
        if ("mappingMongoConverter" == beanName) {
            ((MappingMongoConverter) bean).setTypeMapper(new CustomMongoTypeMapper());
        }
        return bean;
    }
}