How to combine known interface properties with a custom index signature?

The question accepted by the owner (until now) is incorrect.

Here's how you can do it:

You need to make the index signature a union type of all the types that can be contained in the interface:

interface IExample {
    hello?: string;
    moo?: boolean;
    [custom: string]: string | boolean | YourFunctionType;
}

interface YourFunctionType {
    (v?: any): boolean;
}

Please note that I've extracted your function type into a separate interface to improve readability.

Implications:

This means, that the explicitly defined properties are well supported by TS:

const test: IExample = <IExample>{};
test.hello.slice(2); // using a string method on a string --> OK
const isHello = test.hello === true; // ERROR (as expected): === cannot be applied to types string and boolean
const isMoo2 = test.moo === true; // OK

However all properties from the index signature now need to be checked using type guards which adds a little bit of a runtime overhead:

test.callSomething(); // ERROR: type 'string | boolean | YourFunctionType' has no compatible call signatures
if (typeof test.callSomething === 'function') { // alternatively you can use a user defined type guard, like Lodash's _.isFunction() which looks a little bit nicer
    test.callSomething(); // OK
}

On the other hand: the runtime overhead is necessary because it might be that test is accessed like this:

const propertyName: string = 'moo';
test[propertyName](); // ERROR: resolves to a boolean at runtime, not a function ...

// ... so to be sure that an arbitrary propertyName can really be called we need to check:
const propertyName2: string = 'arbitraryPropertyName';
const maybeFunction = test[propertyName2];
if (typeof maybeFunction === 'function') {
    maybeFunction(); // OK
}

This is not possible, by design https://basarat.gitbooks.io/typescript/docs/types/index-signatures.html

As soon as you have a string index signature, all explicit members must also conform to that index signature. This is to provide safety so that any string access gives the same result.

The only way to get around it is to exploit that each interface can have 2 separate index signatures, one for string and number

In you example hello and moo make the string index unusable, but you can hijack the number index for the custom methods

interface IExample {
  hello?: string
  moo?: boolean
  [custom: number]: (v?: any) => boolean
}

const myBasic: IExample = {moo: false}
// -> ✅ Valid! Using known keys

const myValid: IExample = {hello: 'world', 2: () => true}
// -> ✅ Valid! "customYo" is a function returning a bool. Good job!

const myInvalid: IExample = {hello: 'world', 2: 'yo!'}
// -> ☠️ Invalid! "customYo" must be a function returning a boolean

This works but is hardly an acceptable interface as would lead to unintuitive functions and you would have to call them by array notation

myValid.7() // Cannot invoke an expression whose type lacks a call signature. Type 'Number' has no compatible call signatures.
myValid[2]() // works (but ewwwww what is this!!!)
// could alias to more readable locals later but still ewwwwww!!! 
const myCustomFunc = myValid[2]
myCustomFunc() // true

This also has the caveat that the type returned from a numeric indexer must be a subtype of the type returned from the string indexer. This is because when indexing with a number, javascript will convert the number to a string before indexing into an object

In this case you have no explicit string indexer, so the string index type is the default any which the numeric indexer type can conform to

IMPORTANT This is just for the science, I don't recommend this as a real life approach!