I want to execute a defined class function from an Element inside my Web Component:
customElements.define('first-component', class FirstComponent extends HTMLElement {
    constructor() {
        super();
     }
     log() {
        console.log('Well Done!')
     }
     connectedCallback() {
        this.innerHTML = '<button onclick="log()">Do it</button>'
     }
});
State right now: ReferenceError: log is not defined
With parentElement, or closest()
In order to call the log() method of the custom element, you'll have to get a reference on it.
In your example, the custom element is the parent element of the <button> element, so you should call the parentElement property of the button as already stated by @Smankusors:
<button onclick="this.parentElement.log()>Do it</button>
With getRootNode()
Alternately, in a more complex DOM tree, and if a Shadow DOM is used, you can use getRootNode() combined with host to get the custom element reference.
customElements.define('first-component', class FirstComponent extends HTMLElement {
     log() {
        console.log('Well Done!')
     }
     connectedCallback() {
        this.attachShadow({mode: 'open'})
            .innerHTML = '<button onclick="this.getRootNode().host.log()">Do it</button>'
     }
})
<first-component></first-component>
With a unique identifier
You can also call the custom element by its id property (if it has one) :
customElements.define('first-component', class FirstComponent extends HTMLElement {
     log() {
        console.log('Well Done!')
     }
     connectedCallback() {
        if (!this.id)
            this.id = "_id"
        this.innerHTML = `<button onclick="${this.id}.log()">Do it</button>`
     }
})
<first-component></first-component>
With handleEvent()
For security reasons, you can avoid inline script and implement the handleEvent() method, then call inside it a specific method depending on some  criterions :
customElements.define('first-component', class FirstComponent extends HTMLElement {
    log() {
        console.log('Well Done!')
    }
     
    handleEvent(ev) {
        if (ev.target.innerText == 'Do it')
            this.log()
    }
    connectedCallback() {
        this.innerHTML = '<button>Do it</button>'
        this.addEventListener('click', this)
    }
})
<first-component></first-component>
That shouldn't be log(), but this.log(), because that log function scope is only that element, not in window scope, so your code should be
customElements.define('first-component', class FirstComponent extends HTMLElement {
    constructor() {
        super();
     }
     log() {
        console.log('Well Done!')
     }
     connectedCallback()
        this.innerHTML = '<button onclick="this.parentElement.log()">Do it</button>'
     }
});
-- EDIT --
Sorry, my mistake, I just saw that you added button inside custom element, well... It should be this.parentElement.log() if you still want to prefer inline
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