In medium saucepan, combine strawberries, sugar and lemon juice. Bring to a boil over medium-high heat, stirring often. Reduce heat to low and simmer 10 min., or until jam has thickened and coats of spoon. Crush strawberry mixture with potato masher to break up berries further. Cool jam slightly, cover and refrigerate.
Preheat oven to 350°F (180°C). Line two baking sheets with parchment paper. In large bowl, cream butter and brown sugar until fluffy, about 1 min. Mix in egg and vanilla extract. Stir in flours, baking soda and salt; mix well. Use hands if necessary to form dough. Roll level 1-tbsp (15-mL) portions of dough into balls; place onto prepared baking sheets. Make 30 balls. Using index finger, press large well in the middle of each. Bake 10 to 12 min., or until just turning golden around edges.
As soon as cookies come out of oven (they will be soft), use the end of a wooden spoon handle to re-indent wells, making 1/4-in. (5-mm) deep wells. Fill each well with 1/2 tsp (2 mL) reserved strawberry jam. Top each cookie with a marshmallow half, cut-side down. Place cookies back on lined baking sheets and bake about 2 min., or until marshmallows are melted. Using back of small spoon, press down on softened marshmallow and spread across cookie base. Cool completely on rack set over baking sheet.
Meanwhile, in large microwaveable bowl, combine chocolate chips and coconut oil. Microwave on HIGH 2 min., stirring every 30 sec., until melted. To cover tops of cookies in chocolate, place each -- marshmallow-side down -- onto a fork (use a second fork to guide) and dunk into melted chocolate mixture. Coat marshmallow and sides of cookies, but not the cookie bottom. Place onto rack, on cookie bottoms, allowing excess chocolate to drip off. Chill at least 30 min. to set chocolate. Cover and keep chilled until serving.
As a shortcut, skip step one and use your favourite store-bought jam instead.