class StartViewModel() : BaseViewModel() {
    sealed class Input : IInput {
        object ButtonClicked : Input()
    }

    override fun handleInput(input: IInput) { //I want this to be of the type Input, instead of the interface      
    }
}

abstract class BaseViewModel {
    interface IInput
    protected abstract fun handleInput(input: IInput)

    init {
        handleInput(something that implements IInput)       
    }
}

class StartViewModel() : BaseViewModel<StartViewModel.Input>() {
    sealed class Input : IInput {
        object ButtonClicked: Input()
    }

    override fun handleInput(input: Input) {

    }
}

abstract class BaseViewModel<T : BaseViewModel.IInput> {
    interface IInput
    protected abstract fun handleInput(input: T)
}