Slice the pork tenderloin into 3/4 inch thick pieces.
In a shallow bowl, mix together all purpose flour, seasoned salt and black pepper until blended. Reserve 1/4 cup for the gravy and set aside.
Use the remaining 1/2 cup to dust both sides of the sliced pork tenderloin.
Heat 1/4 cup of olive oil and 3 Tbsp of butter in a large skillet over medium-high heat.
Brown the tenderloin in batches cooking for around 4 minutes on each side. Adjust depending on thickness. Remove to a platter and keep warm.
To make grav: Reserve 2 Tbsp of pan drippings and add 3 Tbsp of butter.
Sprinkle the 1/4 cup reserved flour into the pan and stir to combine. Cook for about 1 minute scraping any brown bits from bottom of pan.
Gradually whisk in the milk, tarragon and poultry seasoning.
After all of the milk has been added, bring to a boil to thicken, then immediately lower the heat whisking constantly. Let the gravy slowly bubble for 5 minutes, stirring occasionally, over low heat. Adjust salt and black pepper to your taste.
You may adjust the consistency adding more milk to thin, if desired. Serve immediately drizzled over pork tenderloin.