Using:
Texture2D texture = this.Content.Load<Texture2D>("MyTexture");
Will default texture usage to "Immutable" and will only allow binding as Shader View.
In order to generate MipMaps, usage needs to be Default and Binding as both ShaderView/RenderView.
Now you have a few options:
1/Preprocess your textures as dds with mipmaps, loader would take this into account.
TexConv can do that for you. (use -m to specify level count).
2/Load your texture as above, create a second texture using
Texture2D texturewithmips = Texture2D.New(device, texture.Width, texture.Height, MipMapCount.Auto, texture.Format,
TextureFlags.ShaderResource | TextureFlags.RenderTarget,
1,Direct3D11.ResourceUsage.Default);
Now you need to copy the first mip, using :
device.Copy(texture, 0, null, t2, 0);
You can now use :
t2.GenerateMipMaps(this.GraphicsDevice);
3/Since with method above you kinda lose the content manager (with auto caches for you).
You can modify the TextureContentReader class to do that for you, by adding more options for texture loading.
If you need more help feel free.