THe speed of an induction motor is dependent on the frequency of the input waveform. Do not try to PWM it like a DC brushed or brushless motor to slow the motor down. The speeds of those motors is dependent on average voltage seen which is what PWM does and is the limit of what a 555 timer is capable of. Not a microcontroller though, but the microcontroller is not the problem in this case- it's all the power circuitry required to pull off the solutions I am about to talk about is.
Since the speed of induction motors is dependent on the voltage and frequency of the AC signal, you need a drive that can produce a wide range of voltages and more importantly frequencies. These called variable frequency drives and are the most complex of conventional motor drives. Many (if not most) do incorporate microcontrollers. Then there are even more complicated weird kinds that can convert AC of one voltage and frequency directly into AC of another voltage and frequency...really...strange things.
The best you can do with a 555 timer or a microcontroller (without extensive power circuitry and coding) is turning the motor on and off so it alternates between full speed and no speed which is not advisable unless you are talking about infrequent switchings (like on the order of once a minute or more).
Easiest thing to do would be to change the gear ratio. If you want an electrical challenge, then replace the motor with a brushed DC motor. It sounds like you only need unidirectional speed control so that means a single-transistor motor drieer being controlled by a 555 timer wired up as a PWM generator or a microcontroller doing the same job (and maybe a gate driver to help the 555 timer or MCU drive the transistor. THis should be completely within your capability as is a rather nice starter project.
Beyond that are things like H-bridges for bidirecitonal speed control of brushed DC motors. Then there are trapezoidal synchronous motor drivers followed by sinusoidal synchronous motor drivers (which with some modification in the control loop are basically what is required for induction motors.
Naming Convention FIasco:Induction and synchronous motors both contain no brushes, but normally when someone says brushless motor they are talking about a specific class of synchronous motor that uses permanent magnets and is designed to run off trapesoidal waveforms. And even those these are synchronous motors, many times when someone says synchronous motor they are referring to a specific class of synchronous motors that use field windings instead of permanent magnets and are designed to run off sinusoidal waveforms tend to be called synchronous motors.