In a small saucepan, stir the shallot, peppers, butter, red pepper flakes, sugar, and vinegar over medium heat until the sugar is dissolved and the butter is melted.
Bring to a boil, then reduce heat to low. Simmer for about 30 minutes, stirring occasionally, until the jelly has reduced and somewhat thickened.
Add the lemon juice and chopped strawberries (or cornstarch mixture), and cook over low heat until the strawberries are broken down and the jelly has thickened, about 25–30 more minutes. Remove from heat and let cool. The jelly will continue to thicken as it cools, but if it’s still a little watery you can return to the heat for a few more minutes (or add more cornstarch).
Store in a lidded glass jar in the refrigerator for as long as three months.