The first thing I would say is don't do this, just define the function from your export script and remove all this complexity. If you really really really want to you can access the parent session state and call New-Item on the function: provider through that

Function test-function {
    'abc'

    $parent = (Get-Variable -Scope 1 -Name ExecutionContext -ValueOnly).SessionState
    $null = $parent.InvokeProvider.Item.New(
        <# path #>         'function:test-function',
        <# name #>         '',
        <# itemTypeName #> '',
        <# content #>      { "def" },
        <# force #>        $true)
}

test-function
# abc

test-function
# def

If the function is an advanced function you have an easier way to access the parent session state through $PSCmdlet.SessionState

Function test-function {
    [CmdletBinding()]
    param ()

    'abc'

    $null = $PSCmdlet.SessionState.InvokeProvider.Item.New(
        <# path #>         'function:test-function',
        <# name #>         '',
        <# itemTypeName #> '',
        <# content #>      { "def" },
        <# force #>        $true)
}

In general self modifying code is considered a bad thing.

The traditional approach is to have a global static where if it not set you run your initialisation , then set it once your initialisation has completed.

You also have to cater for the first time run occurring from multithreaded code so need to guard the initialisation to ensure it happens just once using a mutex or critical section..