Part One

Step 1 – Creating the Edges

Using the Lasso Tool, make a selection around the inside of the parchment that will give it jagged edges.

Then apply an Add Layer Mask at the bottom of the layer pallet.

Step 2 – Creating the Outer Crisp

In order to get the burnt effect, we need to create a dark outer edge around the parchment.

Create an New Layer

To do this, use a really dark brown color like #211a0a and hard small brushes around 3-5px to create an effect like below.

Then copy the Layer Mask from the Parchment Paper layer and past it onto the painted layer.

Step 3 – Burning the Edges

To make the burn look more realistic we need to have a transition from the dirty parchment to the burnt edges.

Duplicate (Right Click > Duplicate Layer) the layer containing your crispy dark edge.

Then apply a Gaussian Blur (Filter > Blur > Gaussian Blur) of 2.

Set the layer to Darken, and make a selection of the layer mask set on the Parchment group.

Then apply the same layer mask to your current layer.

Step 3 – Add Your Ligature Logo

1. Copy your Illustrator logo (Lone star)

Step 4 – Grunge Your Logo

1. Add A layer mask
   
   

1. Now choose from the Brush tool the brush you made
   
2. Paint in your layer mask with your brush

Step 5 – Final Touches

1. Add Text and then repeat steps above
   (layer mask, paint with your brush)

(extra credit)
Incredibly Realistic Burnt Parchment in Photoshop