desktop.MainWindow = new MainWindow
{
    DataContext = new MainWindowViewModel()
};

desktop.MainWindow = new MainWindow
{
    DataContext = new MainWindowViewModel()
};

//ToDoListView.axaml
<UserControl //boiler plate stff
             x:Class="testAvaloniaApplication1.Views.ToDoListView"
             x:DataType="vm:ToDoListViewModel">
    <DockPanel>
        <Button DockPanel.Dock="Bottom"
                HorizontalAlignment="Stretch"
                HorizontalContentAlignment="Center"
                Content="Add an item"/>
        <ItemsControl ItemsSource="{Binding ListItems}">
            <ItemsControl.ItemTemplate>
                <DataTemplate>
                    <CheckBox Margin="4"
                              IsChecked="{Binding IsChecked}"
                              Content="{Binding Description}"/>
                </DataTemplate>
            </ItemsControl.ItemTemplate>
        </ItemsControl>
    </DockPanel>
</UserControl>

//ToDoListView.axaml
<UserControl //boiler plate stff
             x:Class="testAvaloniaApplication1.Views.ToDoListView"
             x:DataType="vm:ToDoListViewModel">
    <DockPanel>
        <Button DockPanel.Dock="Bottom"
                HorizontalAlignment="Stretch"
                HorizontalContentAlignment="Center"
                Content="Add an item"/>
        <ItemsControl ItemsSource="{Binding ListItems}">
            <ItemsControl.ItemTemplate>
                <DataTemplate>
                    <CheckBox Margin="4"
                              IsChecked="{Binding IsChecked}"
                              Content="{Binding Description}"/>
                </DataTemplate>
            </ItemsControl.ItemTemplate>
        </ItemsControl>
    </DockPanel>
</UserControl>

using testAvaloniaApplication1.DataModels;

namespace testAvaloniaApplication1.ViewModels
{
    public class MainWindowViewModel : ViewModelBase
    {
        //Depends on ToDoListServices
        public ToDoListViewModel ToDoList { get; }
        public MainWindowViewModel()
        {
            var service = new ToDoListService();
            ToDoList = new ToDoListViewModel(service.GetItems());
        }
    }
}

using testAvaloniaApplication1.DataModels;

namespace testAvaloniaApplication1.ViewModels
{
    public class MainWindowViewModel : ViewModelBase
    {
        //Depends on ToDoListServices
        public ToDoListViewModel ToDoList { get; }
        public MainWindowViewModel()
        {
            var service = new ToDoListService();
            ToDoList = new ToDoListViewModel(service.GetItems());
        }
    }
}

using System.Collections.Generic;
using System.Collections.ObjectModel;
using testAvaloniaApplication1.DataModels;

namespace testAvaloniaApplication1.ViewModels;

public class ToDoListViewModel : ViewModelBase
{
    public ObservableCollection<ToDoItem> ListItems { get; set; }
    public ToDoListViewModel(IEnumerable<ToDoItem> items)
    {
        ListItems = new ObservableCollection<ToDoItem>(items);
    }
}

using System.Collections.Generic;
using System.Collections.ObjectModel;
using testAvaloniaApplication1.DataModels;

namespace testAvaloniaApplication1.ViewModels;

public class ToDoListViewModel : ViewModelBase
{
    public ObservableCollection<ToDoItem> ListItems { get; set; }
    public ToDoListViewModel(IEnumerable<ToDoItem> items)
    {
        ListItems = new ObservableCollection<ToDoItem>(items);
    }
}