On a cutting board, chop whole or halved pecans into small pieces, but not super fine. I like slightly bigger pieces, but it's a personal preference.
Place pecans in a microwaveable dish (I like to use a glass pie plate) with the 3 tablespoons of butter. If you like things a little more salty, you can always add a bit of sea salt on top of the pecans too.
Cook for 4 - 7 minutes, stirring twice. Watch the pecans VERY carefully so they don't burn! It can happen pretty quickly, so just keep a close eye on them. (Microwaves will vary–start with the least amount of time, then check them before adding more time.)
In another microwave-safe bowl (I like using glass bowls–a glass batter bowl is my favorite), place remaining butter and heat until melted.
Whisk in brown sugar, flour, corn syrup, and evaporated milk until blended.
Cook on high 6-8 minutes, stirring 2-3 times, until the sugar is dissolved. It should be amber in color.
Add in the toasted pecans, and stir the mixture well.
Pour into jars. If giving as gifts, I like the wide-mouth half-pint jars, which fit 1 cup each. For home use, I use bigger jars. Makes approximately 3 c. of sauce.