Thank you for the replies Art.
1) The type of breaker that you are referring to is a tandem or mini breaker. It installs on the panel as a full size breaker but is split into 2 smaller breakers as you mention.
2) Depending upon the age of the home, kitchen counter tops require (2) two dedicated 20 amp circuits and also need to be GFCI protected.
How old is the home?
What is the amperage of the breaker that the receptacles are connected to? Is the tandem breaker 15/15 or 15/20 or 20/20 amps?
Have the toaster and kettle worked properly on this receptacle and the problem recently started?
3) How many receptacles are on this circuit? If more than 1 receptacle is on the circuit, can you plug the appliance into another receptacle that is on the same circuit to determine if the breaker still trips? In other words, does the trouble follow or does the trouble go away?
4) We will need confirmation if the receptacle is GFCI protected or not. If the receptacle is GFCI protected, it is possible that the GFCI tripped and the circuit breaker did not? You would need to confirm.